Numerical methods of statistics /:
This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mat...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
2011.
|
| Ausgabe: | 2nd ed. |
| Schriftenreihe: | Cambridge series on statistical and probabilistic mathematics ;
32. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book offers a basic background in numerical analysis that emphasizes issues important to statisticians. The next several chapters cover a broad array of statistical tools, such as maximum likelihood and nonlinear regression. The author also treats the application of numerical tools; numerical integration and random number generation are explained in a unified manner reflecting complementary views of Monte Carlo methods. Each chapter contains exercises that range from simple questions to research problems. Most of the examples are accompanied by demonstration and source code available from the author's website. New in this second edition are demonstrations coded in R, as well as new sections on linear programming and the Nelder-Mead search algorithm. |
| Beschreibung: | 1 online resource (xvi, 447 pages :) |
| Bibliographie: | Includes bibliographical references and indexes. |
| ISBN: | 9781139082112 1139082116 9781139079846 1139079840 9781139077552 1139077554 9780511977176 0511977174 1107213894 9781107213890 1283112329 9781283112321 9786613112323 6613112321 1139075292 9781139075299 1139069527 9781139069526 |
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| 100 | 1 | |a Monahan, John F. |0 http://id.loc.gov/authorities/names/n83028711 | |
| 245 | 1 | 0 | |a Numerical methods of statistics / |c John F. Monahan. |
| 250 | |a 2nd ed. | ||
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c 2011. | ||
| 300 | |a 1 online resource (xvi, 447 pages :) | ||
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| 490 | 1 | |a Cambridge series in statistical and probabilistic mathematics ; |v [32] | |
| 504 | |a Includes bibliographical references and indexes. | ||
| 505 | 0 | 0 | |g 1. |t Algorithms and Computers -- |g 1.1. |t Introduction -- |g 1.2. |t Computers -- |g 1.3. |t Software and Computer Languages -- |g 1.4. |t Data Structures -- |g 1.5. |t Programming Practice -- |g 1.6. |t Some Comments on R -- |t References -- |g 2. |t Computer Arithmetic -- |g 2.1. |t Introduction -- |g 2.2. |t Positional Number Systems -- |g 2.3. |t Fixed Point Arithmetic -- |g 2.4. |t Floating Point Representations -- |g 2.5. |t Living with Floating Point Inaccuracies -- |g 2.6. |t The Pale and Beyond -- |g 2.7. |t Conditioned Problems and Stable Algorithms -- |t Programs and Demonstrations -- |t Exercises -- |t References -- |g 3. |t Matrices and Linear Equations -- |g 3.1. |t Introduction -- |g 3.2. |t Matrix Operations -- |g 3.3. |t Solving Triangular Systems -- |g 3.4. |t Gaussian Elimination -- |g 3.5. |t Cholesky Decomposition -- |g 3.6. |t Matrix Norms -- |g 3.7. |t Accuracy and Conditioning -- |g 3.8. |t Matrix Computations in R -- |t Programs and Demonstrations -- |t Exercises -- |t References. |
| 505 | 0 | 0 | |g 4. |t More Methods for Solving Linear Equations -- |g 4.1. |t Introduction -- |g 4.2. |t Full Elimination with Complete Pivoting -- |g 4.3. |t Banded Matrices -- |g 4.4. |t Applications to ARMA Time-Series Models -- |g 4.5. |t Toeplitz Systems -- |g 4.6. |t Sparse Matrices -- |g 4.7. |t Iterative Methods -- |g 4.8. |t Linear Programming -- |t Programs and Demonstrations -- |t Exercises -- |t References -- |g 5. |t Regression Computations -- |g 5.1. |t Introduction -- |g 5.2. |t Condition of the Regression Problem -- |g 5.3. |t Solving the Normal Equations -- |g 5.4. |t Gram-Schmidt Orthogonalization -- |g 5.5. |t Householder Transformations -- |g 5.6. |t Householder Transformations for Least Squares -- |g 5.7. |t Givens Transformations -- |g 5.8. |t Givens Transformations for Least Squares -- |g 5.9. |t Regression Diagnostics -- |g 5.10. |t Hypothesis Tests -- |g 5.11. |t Conjugate Gradient Methods -- |g 5.12. |t Doolittle, the Sweep, and All Possible Regressions -- |g 5.13. |t Alternatives to Least Squares -- |g 5.14. |t Comments -- |t Programs and Demonstrations -- |t Exercises -- |t References. |
| 505 | 0 | 0 | |g 6. |t Eigenproblems -- |g 6.1. |t Introduction -- |g 6.2. |t Theory -- |g 6.3. |t Power Methods -- |g 6.4. |t The Symmetric Eigenproblem and Tridiagonalization -- |g 6.5. |t The QR Algorithm -- |g 6.6. |t Singular Value Decomposition -- |g 6.7. |t Applications -- |g 6.8. |t Complex Singular Value Decomposition -- |t Programs and Demonstrations -- |t Exercises -- |t References -- |g 7. |t Functions: Interpolation, Smoothing, and Approximation -- |g 7.1. |t Introduction -- |g 7.2. |t Interpolation -- |g 7.3. |t Interpolating Splines -- |g 7.4. |t Curve Fitting with Splines: Smoothing and Regression -- |g 7.5. |t Mathematical Approximation -- |g 7.6. |t Practical Approximation Techniques -- |g 7.7. |t Computing Probability Functions -- |t Programs and Demonstrations -- |t Exercises -- |t References -- |g 8. |t Introduction to Optimization and Nonlinear Equations -- |g 8.1. |t Introduction -- |g 8.2. |t Safe Univariate Methods: Lattice Search, Golden Section, and Bisection -- |g 8.3. |t Root Finding -- |g 8.4. |t First Digression: Stopping and Condition. |
| 505 | 0 | 0 | |g 8.5. |t Multivariate Newton's Methods -- |g 8.6. |t Second Digression: Numerical Differentiation -- |g 8.7. |t Minimization and Nonlinear Equations -- |g 8.8. |t Condition and Scaling -- |g 8.9. |t Implementation -- |g 8.10. |t A Non-Newton Method: Nelder-Mead -- |t Programs and Demonstrations -- |t Exercises -- |t References -- |g 9. |t Maximum Likelihood and Nonlinear Regression -- |g 9.1. |t Introduction -- |g 9.2. |t Notation and Asymptotic Theory of Maximum Likelihood -- |g 9.3. |t Information, Scoring, and Variance Estimates -- |g 9.4. |t An Extended Example -- |g 9.5. |t Concentration, Iteration, and the EM Algorithm -- |g 9.6. |t Multiple Regression in the Context of Maximum Likelihood -- |g 9.7. |t Generalized Linear Models -- |g 9.8. |t Nonlinear Regression -- |g 9.9. |t Parameterizations and Constraints -- |t Programs and Demonstrations -- |t Exercises -- |t References -- |g 10. |t Numerical Integration and Monte Carlo Methods -- |g 10.1. |t Introduction -- |g 10.2. |t Motivating Problems -- |g 10.3. |t One-Dimensional Quadrature. |
| 505 | 0 | 0 | |g 10.4. |t Numerical Integration in Two or More Variables -- |g 10.5. |t Uniform Pseudorandom Variables -- |g 10.6. |t Quasi-Monte Carlo Integration -- |g 10.7. |t Strategy and Tactics -- |t Programs and Demonstrations -- |t Exercises -- |t References -- |g 11. |t Generating Random Variables from Other Distributions -- |g 11.1. |t Introduction -- |g 11.2. |t General Methods for Continuous Distributions -- |g 11.3. |t Algorithms for Continuous Distributions -- |g 11.4. |t General Methods for Discrete Distributions -- |g 11.5. |t Algorithms for Discrete Distributions -- |g 11.6. |t Other Randomizations -- |g 11.7. |t Accuracy in Random Number Generation -- |t Programs and Demonstrations -- |t Exercises -- |t References -- |g 12. |t Statistical Methods for Integration and Monte Carlo -- |g 12.1. |t Introduction -- |g 12.2. |t Distribution and Density Estimation -- |g 12.3. |t Distributional Tests -- |g 12.4. |t Importance Sampling and Weighted Observations -- |g 12.5. |t Testing Importance Sampling Weights -- |g 12.6. |t Laplace Approximations. |
| 505 | 0 | 0 | |g 12.7. |t Randomized Quadrature -- |g 12.8. |t Spherical-Radial Methods -- |t Programs and Demonstrations -- |t Exercises -- |t References -- |g 13. |t Markov Chain Monte Carlo Methods -- |g 13.1. |t Introduction -- |g 13.2. |t Markov Chains -- |g 13.3. |t Gibbs Sampling -- |g 13.4. |t Metropolis-Hastings Algorithm -- |g 13.5. |t Time-Series Analysis -- |g 13.6. |t Adaptive Acceptance/Rejection -- |g 13.7. |t Diagnostics -- |t Programs and Demonstrations -- |t Exercises -- |t References -- |g 14. |t Sorting and Fast Algorithms -- |g 14.1. |t Introduction -- |g 14.2. |t Divide and Conquer -- |g 14.3. |t Sorting Algorithms -- |g 14.4. |t Fast Order Statistics and Related Problems -- |g 14.5. |t Fast Fourier Transform -- |g 14.6. |t Convolutions and the Chirp-z Transform -- |g 14.7. |t Statistical Applications of the FFT -- |g 14.8. |t Combinatorial Problems -- |t Programs and Demonstrations -- |t Exercises -- |t References. |
| 588 | 0 | |a Print version record. | |
| 520 | |a This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book offers a basic background in numerical analysis that emphasizes issues important to statisticians. The next several chapters cover a broad array of statistical tools, such as maximum likelihood and nonlinear regression. The author also treats the application of numerical tools; numerical integration and random number generation are explained in a unified manner reflecting complementary views of Monte Carlo methods. Each chapter contains exercises that range from simple questions to research problems. Most of the examples are accompanied by demonstration and source code available from the author's website. New in this second edition are demonstrations coded in R, as well as new sections on linear programming and the Nelder-Mead search algorithm. | ||
| 546 | |a English. | ||
| 650 | 0 | |a Mathematical statistics |x Data processing. |0 http://id.loc.gov/authorities/subjects/sh85082137 | |
| 650 | 0 | |a Numerical analysis. |0 http://id.loc.gov/authorities/subjects/sh85093237 | |
| 650 | 6 | |a Statistique mathématique |x Informatique. | |
| 650 | 6 | |a Analyse numérique. | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x General. |2 bisacsh | |
| 650 | 7 | |a Mathematical statistics |x Data processing |2 fast | |
| 650 | 7 | |a Numerical analysis |2 fast | |
| 655 | 0 | |a Electronic book. | |
| 655 | 4 | |a Electronic books. | |
| 758 | |i has work: |a Numerical methods of statistics (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGWTFhK7Pp6RRVRv4bkWCP |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Monahan, John F. |t Numerical methods of statistics. |b 2nd ed. |d Cambridge ; New York : Cambridge University Press, ©2011 |z 9780521191586 |w (DLC) 2011287063 |w (OCoLC)708741707 |
| 830 | 0 | |a Cambridge series on statistical and probabilistic mathematics ; |v 32. |0 http://id.loc.gov/authorities/names/n96064948 | |
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Datensatz im Suchindex
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|---|---|
| _version_ | 1813903404849692672 |
| adam_text | |
| any_adam_object | |
| author | Monahan, John F. |
| author_GND | http://id.loc.gov/authorities/names/n83028711 |
| author_facet | Monahan, John F. |
| author_role | |
| author_sort | Monahan, John F. |
| author_variant | j f m jf jfm |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA276 |
| callnumber-raw | QA276.4 .M66 2011eb |
| callnumber-search | QA276.4 .M66 2011eb |
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| collection | ZDB-4-EBA |
| contents | Algorithms and Computers -- Introduction -- Computers -- Software and Computer Languages -- Data Structures -- Programming Practice -- Some Comments on R -- References -- Computer Arithmetic -- Positional Number Systems -- Fixed Point Arithmetic -- Floating Point Representations -- Living with Floating Point Inaccuracies -- The Pale and Beyond -- Conditioned Problems and Stable Algorithms -- Programs and Demonstrations -- Exercises -- Matrices and Linear Equations -- Matrix Operations -- Solving Triangular Systems -- Gaussian Elimination -- Cholesky Decomposition -- Matrix Norms -- Accuracy and Conditioning -- Matrix Computations in R -- References. More Methods for Solving Linear Equations -- Full Elimination with Complete Pivoting -- Banded Matrices -- Applications to ARMA Time-Series Models -- Toeplitz Systems -- Sparse Matrices -- Iterative Methods -- Linear Programming -- Regression Computations -- Condition of the Regression Problem -- Solving the Normal Equations -- Gram-Schmidt Orthogonalization -- Householder Transformations -- Householder Transformations for Least Squares -- Givens Transformations -- Givens Transformations for Least Squares -- Regression Diagnostics -- Hypothesis Tests -- Conjugate Gradient Methods -- Doolittle, the Sweep, and All Possible Regressions -- Alternatives to Least Squares -- Comments -- Eigenproblems -- Theory -- Power Methods -- The Symmetric Eigenproblem and Tridiagonalization -- The QR Algorithm -- Singular Value Decomposition -- Applications -- Complex Singular Value Decomposition -- Functions: Interpolation, Smoothing, and Approximation -- Interpolation -- Interpolating Splines -- Curve Fitting with Splines: Smoothing and Regression -- Mathematical Approximation -- Practical Approximation Techniques -- Computing Probability Functions -- Introduction to Optimization and Nonlinear Equations -- Safe Univariate Methods: Lattice Search, Golden Section, and Bisection -- Root Finding -- First Digression: Stopping and Condition. Multivariate Newton's Methods -- Second Digression: Numerical Differentiation -- Minimization and Nonlinear Equations -- Condition and Scaling -- Implementation -- A Non-Newton Method: Nelder-Mead -- Maximum Likelihood and Nonlinear Regression -- Notation and Asymptotic Theory of Maximum Likelihood -- Information, Scoring, and Variance Estimates -- An Extended Example -- Concentration, Iteration, and the EM Algorithm -- Multiple Regression in the Context of Maximum Likelihood -- Generalized Linear Models -- Nonlinear Regression -- Parameterizations and Constraints -- Numerical Integration and Monte Carlo Methods -- Motivating Problems -- One-Dimensional Quadrature. Numerical Integration in Two or More Variables -- Uniform Pseudorandom Variables -- Quasi-Monte Carlo Integration -- Strategy and Tactics -- Generating Random Variables from Other Distributions -- General Methods for Continuous Distributions -- Algorithms for Continuous Distributions -- General Methods for Discrete Distributions -- Algorithms for Discrete Distributions -- Other Randomizations -- Accuracy in Random Number Generation -- Statistical Methods for Integration and Monte Carlo -- Distribution and Density Estimation -- Distributional Tests -- Importance Sampling and Weighted Observations -- Testing Importance Sampling Weights -- Laplace Approximations. Randomized Quadrature -- Spherical-Radial Methods -- Markov Chain Monte Carlo Methods -- Markov Chains -- Gibbs Sampling -- Metropolis-Hastings Algorithm -- Time-Series Analysis -- Adaptive Acceptance/Rejection -- Diagnostics -- Sorting and Fast Algorithms -- Divide and Conquer -- Sorting Algorithms -- Fast Order Statistics and Related Problems -- Fast Fourier Transform -- Convolutions and the Chirp-z Transform -- Statistical Applications of the FFT -- Combinatorial Problems -- |
| ctrlnum | (OCoLC)732958873 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2nd ed. |
| format | Electronic eBook |
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code="a">MAT</subfield><subfield code="x">029000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">519.5</subfield><subfield code="2">22</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Monahan, John F.</subfield><subfield code="0">http://id.loc.gov/authorities/names/n83028711</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Numerical methods of statistics /</subfield><subfield code="c">John F. Monahan.</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2nd ed.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Cambridge ;</subfield><subfield code="a">New York :</subfield><subfield code="b">Cambridge University Press,</subfield><subfield code="c">2011.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xvi, 447 pages :)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="347" ind1=" " ind2=" "><subfield code="a">data file</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Cambridge series in statistical and probabilistic mathematics ;</subfield><subfield code="v">[32]</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and indexes.</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="g">1.</subfield><subfield code="t">Algorithms and Computers --</subfield><subfield code="g">1.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">1.2.</subfield><subfield code="t">Computers --</subfield><subfield code="g">1.3.</subfield><subfield code="t">Software and Computer Languages --</subfield><subfield code="g">1.4.</subfield><subfield code="t">Data Structures --</subfield><subfield code="g">1.5.</subfield><subfield code="t">Programming Practice --</subfield><subfield code="g">1.6.</subfield><subfield code="t">Some Comments on R --</subfield><subfield code="t">References --</subfield><subfield code="g">2.</subfield><subfield code="t">Computer Arithmetic --</subfield><subfield code="g">2.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">2.2.</subfield><subfield code="t">Positional Number Systems --</subfield><subfield code="g">2.3.</subfield><subfield code="t">Fixed Point Arithmetic --</subfield><subfield code="g">2.4.</subfield><subfield code="t">Floating Point Representations --</subfield><subfield code="g">2.5.</subfield><subfield code="t">Living with Floating Point Inaccuracies --</subfield><subfield code="g">2.6.</subfield><subfield code="t">The Pale and Beyond --</subfield><subfield code="g">2.7.</subfield><subfield code="t">Conditioned Problems and Stable Algorithms --</subfield><subfield code="t">Programs and Demonstrations --</subfield><subfield code="t">Exercises --</subfield><subfield code="t">References --</subfield><subfield code="g">3.</subfield><subfield code="t">Matrices and Linear Equations --</subfield><subfield code="g">3.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">3.2.</subfield><subfield code="t">Matrix Operations --</subfield><subfield code="g">3.3.</subfield><subfield code="t">Solving Triangular Systems --</subfield><subfield code="g">3.4.</subfield><subfield code="t">Gaussian Elimination --</subfield><subfield code="g">3.5.</subfield><subfield code="t">Cholesky Decomposition --</subfield><subfield code="g">3.6.</subfield><subfield code="t">Matrix Norms --</subfield><subfield code="g">3.7.</subfield><subfield code="t">Accuracy and Conditioning --</subfield><subfield code="g">3.8.</subfield><subfield code="t">Matrix Computations in R --</subfield><subfield code="t">Programs and Demonstrations --</subfield><subfield code="t">Exercises --</subfield><subfield code="t">References.</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="g">4.</subfield><subfield code="t">More Methods for Solving Linear Equations --</subfield><subfield code="g">4.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">4.2.</subfield><subfield code="t">Full Elimination with Complete Pivoting --</subfield><subfield code="g">4.3.</subfield><subfield code="t">Banded Matrices --</subfield><subfield code="g">4.4.</subfield><subfield code="t">Applications to ARMA Time-Series Models --</subfield><subfield code="g">4.5.</subfield><subfield code="t">Toeplitz Systems --</subfield><subfield code="g">4.6.</subfield><subfield code="t">Sparse Matrices --</subfield><subfield code="g">4.7.</subfield><subfield code="t">Iterative Methods --</subfield><subfield code="g">4.8.</subfield><subfield code="t">Linear Programming --</subfield><subfield code="t">Programs and Demonstrations --</subfield><subfield code="t">Exercises --</subfield><subfield code="t">References --</subfield><subfield code="g">5.</subfield><subfield code="t">Regression Computations --</subfield><subfield code="g">5.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">5.2.</subfield><subfield code="t">Condition of the Regression Problem --</subfield><subfield code="g">5.3.</subfield><subfield code="t">Solving the Normal Equations --</subfield><subfield code="g">5.4.</subfield><subfield code="t">Gram-Schmidt Orthogonalization --</subfield><subfield code="g">5.5.</subfield><subfield code="t">Householder Transformations --</subfield><subfield code="g">5.6.</subfield><subfield code="t">Householder Transformations for Least Squares --</subfield><subfield code="g">5.7.</subfield><subfield code="t">Givens Transformations --</subfield><subfield code="g">5.8.</subfield><subfield code="t">Givens Transformations for Least Squares --</subfield><subfield code="g">5.9.</subfield><subfield code="t">Regression Diagnostics --</subfield><subfield code="g">5.10.</subfield><subfield code="t">Hypothesis Tests --</subfield><subfield code="g">5.11.</subfield><subfield code="t">Conjugate Gradient Methods --</subfield><subfield code="g">5.12.</subfield><subfield code="t">Doolittle, the Sweep, and All Possible Regressions --</subfield><subfield code="g">5.13.</subfield><subfield code="t">Alternatives to Least Squares --</subfield><subfield code="g">5.14.</subfield><subfield code="t">Comments --</subfield><subfield code="t">Programs and Demonstrations --</subfield><subfield code="t">Exercises --</subfield><subfield code="t">References.</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="g">6.</subfield><subfield code="t">Eigenproblems --</subfield><subfield code="g">6.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">6.2.</subfield><subfield code="t">Theory --</subfield><subfield code="g">6.3.</subfield><subfield code="t">Power Methods --</subfield><subfield code="g">6.4.</subfield><subfield code="t">The Symmetric Eigenproblem and Tridiagonalization --</subfield><subfield code="g">6.5.</subfield><subfield code="t">The QR Algorithm --</subfield><subfield code="g">6.6.</subfield><subfield code="t">Singular Value Decomposition --</subfield><subfield code="g">6.7.</subfield><subfield code="t">Applications --</subfield><subfield code="g">6.8.</subfield><subfield code="t">Complex Singular Value Decomposition --</subfield><subfield code="t">Programs and Demonstrations --</subfield><subfield code="t">Exercises --</subfield><subfield code="t">References --</subfield><subfield code="g">7.</subfield><subfield code="t">Functions: Interpolation, Smoothing, and Approximation --</subfield><subfield code="g">7.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">7.2.</subfield><subfield code="t">Interpolation --</subfield><subfield code="g">7.3.</subfield><subfield code="t">Interpolating Splines --</subfield><subfield code="g">7.4.</subfield><subfield code="t">Curve Fitting with Splines: Smoothing and Regression --</subfield><subfield code="g">7.5.</subfield><subfield code="t">Mathematical Approximation --</subfield><subfield code="g">7.6.</subfield><subfield code="t">Practical Approximation Techniques --</subfield><subfield code="g">7.7.</subfield><subfield code="t">Computing Probability Functions --</subfield><subfield code="t">Programs and Demonstrations --</subfield><subfield code="t">Exercises --</subfield><subfield code="t">References --</subfield><subfield code="g">8.</subfield><subfield code="t">Introduction to Optimization and Nonlinear Equations --</subfield><subfield code="g">8.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">8.2.</subfield><subfield code="t">Safe Univariate Methods: Lattice Search, Golden Section, and Bisection --</subfield><subfield code="g">8.3.</subfield><subfield code="t">Root Finding --</subfield><subfield code="g">8.4.</subfield><subfield code="t">First Digression: Stopping and Condition.</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="g">8.5.</subfield><subfield code="t">Multivariate Newton's Methods --</subfield><subfield code="g">8.6.</subfield><subfield code="t">Second Digression: Numerical Differentiation --</subfield><subfield code="g">8.7.</subfield><subfield code="t">Minimization and Nonlinear Equations --</subfield><subfield code="g">8.8.</subfield><subfield code="t">Condition and Scaling --</subfield><subfield code="g">8.9.</subfield><subfield code="t">Implementation --</subfield><subfield code="g">8.10.</subfield><subfield code="t">A Non-Newton Method: Nelder-Mead --</subfield><subfield code="t">Programs and Demonstrations --</subfield><subfield code="t">Exercises --</subfield><subfield code="t">References --</subfield><subfield code="g">9.</subfield><subfield code="t">Maximum Likelihood and Nonlinear Regression --</subfield><subfield code="g">9.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">9.2.</subfield><subfield code="t">Notation and Asymptotic Theory of Maximum Likelihood --</subfield><subfield code="g">9.3.</subfield><subfield code="t">Information, Scoring, and Variance Estimates --</subfield><subfield code="g">9.4.</subfield><subfield code="t">An Extended Example --</subfield><subfield code="g">9.5.</subfield><subfield code="t">Concentration, Iteration, and the EM Algorithm --</subfield><subfield code="g">9.6.</subfield><subfield code="t">Multiple Regression in the Context of Maximum Likelihood --</subfield><subfield code="g">9.7.</subfield><subfield code="t">Generalized Linear Models --</subfield><subfield code="g">9.8.</subfield><subfield code="t">Nonlinear Regression --</subfield><subfield code="g">9.9.</subfield><subfield code="t">Parameterizations and Constraints --</subfield><subfield code="t">Programs and Demonstrations --</subfield><subfield code="t">Exercises --</subfield><subfield code="t">References --</subfield><subfield code="g">10.</subfield><subfield code="t">Numerical Integration and Monte Carlo Methods --</subfield><subfield code="g">10.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">10.2.</subfield><subfield code="t">Motivating Problems --</subfield><subfield code="g">10.3.</subfield><subfield code="t">One-Dimensional Quadrature.</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="g">10.4.</subfield><subfield code="t">Numerical Integration in Two or More Variables --</subfield><subfield code="g">10.5.</subfield><subfield code="t">Uniform Pseudorandom Variables --</subfield><subfield code="g">10.6.</subfield><subfield code="t">Quasi-Monte Carlo Integration --</subfield><subfield code="g">10.7.</subfield><subfield code="t">Strategy and Tactics --</subfield><subfield code="t">Programs and Demonstrations --</subfield><subfield code="t">Exercises --</subfield><subfield code="t">References --</subfield><subfield code="g">11.</subfield><subfield code="t">Generating Random Variables from Other Distributions --</subfield><subfield code="g">11.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">11.2.</subfield><subfield code="t">General Methods for Continuous Distributions --</subfield><subfield code="g">11.3.</subfield><subfield code="t">Algorithms for Continuous Distributions --</subfield><subfield code="g">11.4.</subfield><subfield code="t">General Methods for Discrete Distributions --</subfield><subfield code="g">11.5.</subfield><subfield code="t">Algorithms for Discrete Distributions --</subfield><subfield code="g">11.6.</subfield><subfield code="t">Other Randomizations --</subfield><subfield code="g">11.7.</subfield><subfield code="t">Accuracy in Random Number Generation --</subfield><subfield code="t">Programs and Demonstrations --</subfield><subfield code="t">Exercises --</subfield><subfield code="t">References --</subfield><subfield code="g">12.</subfield><subfield code="t">Statistical Methods for Integration and Monte Carlo --</subfield><subfield code="g">12.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">12.2.</subfield><subfield code="t">Distribution and Density Estimation --</subfield><subfield code="g">12.3.</subfield><subfield code="t">Distributional Tests --</subfield><subfield code="g">12.4.</subfield><subfield code="t">Importance Sampling and Weighted Observations --</subfield><subfield code="g">12.5.</subfield><subfield code="t">Testing Importance Sampling Weights --</subfield><subfield code="g">12.6.</subfield><subfield code="t">Laplace Approximations.</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="g">12.7.</subfield><subfield code="t">Randomized Quadrature --</subfield><subfield code="g">12.8.</subfield><subfield code="t">Spherical-Radial Methods --</subfield><subfield code="t">Programs and Demonstrations --</subfield><subfield code="t">Exercises --</subfield><subfield code="t">References --</subfield><subfield code="g">13.</subfield><subfield code="t">Markov Chain Monte Carlo Methods --</subfield><subfield code="g">13.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">13.2.</subfield><subfield code="t">Markov Chains --</subfield><subfield code="g">13.3.</subfield><subfield code="t">Gibbs Sampling --</subfield><subfield code="g">13.4.</subfield><subfield code="t">Metropolis-Hastings Algorithm --</subfield><subfield code="g">13.5.</subfield><subfield code="t">Time-Series Analysis --</subfield><subfield code="g">13.6.</subfield><subfield code="t">Adaptive Acceptance/Rejection --</subfield><subfield code="g">13.7.</subfield><subfield code="t">Diagnostics --</subfield><subfield code="t">Programs and Demonstrations --</subfield><subfield code="t">Exercises --</subfield><subfield code="t">References --</subfield><subfield code="g">14.</subfield><subfield code="t">Sorting and Fast Algorithms --</subfield><subfield code="g">14.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">14.2.</subfield><subfield code="t">Divide and Conquer --</subfield><subfield code="g">14.3.</subfield><subfield code="t">Sorting Algorithms --</subfield><subfield code="g">14.4.</subfield><subfield code="t">Fast Order Statistics and Related Problems --</subfield><subfield code="g">14.5.</subfield><subfield code="t">Fast Fourier Transform --</subfield><subfield code="g">14.6.</subfield><subfield code="t">Convolutions and the Chirp-z Transform --</subfield><subfield code="g">14.7.</subfield><subfield code="t">Statistical Applications of the FFT --</subfield><subfield code="g">14.8.</subfield><subfield code="t">Combinatorial Problems --</subfield><subfield code="t">Programs and Demonstrations --</subfield><subfield code="t">Exercises --</subfield><subfield code="t">References.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book offers a basic background in numerical analysis that emphasizes issues important to statisticians. The next several chapters cover a broad array of statistical tools, such as maximum likelihood and nonlinear regression. The author also treats the application of numerical tools; numerical integration and random number generation are explained in a unified manner reflecting complementary views of Monte Carlo methods. Each chapter contains exercises that range from simple questions to research problems. Most of the examples are accompanied by demonstration and source code available from the author's website. 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| genre | Electronic book. Electronic books. |
| genre_facet | Electronic book. Electronic books. |
| id | ZDB-4-EBA-ocn732958873 |
| illustrated | Illustrated |
| indexdate | 2024-10-25T16:18:09Z |
| institution | BVB |
| isbn | 9781139082112 1139082116 9781139079846 1139079840 9781139077552 1139077554 9780511977176 0511977174 1107213894 9781107213890 1283112329 9781283112321 9786613112323 6613112321 1139075292 9781139075299 1139069527 9781139069526 |
| language | English |
| lccn | 2011287063 |
| oclc_num | 732958873 |
| open_access_boolean | |
| owner | MAIN |
| owner_facet | MAIN |
| physical | 1 online resource (xvi, 447 pages :) |
| psigel | ZDB-4-EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Cambridge series on statistical and probabilistic mathematics ; |
| series2 | Cambridge series in statistical and probabilistic mathematics ; |
| spelling | Monahan, John F. http://id.loc.gov/authorities/names/n83028711 Numerical methods of statistics / John F. Monahan. 2nd ed. Cambridge ; New York : Cambridge University Press, 2011. 1 online resource (xvi, 447 pages :) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Cambridge series in statistical and probabilistic mathematics ; [32] Includes bibliographical references and indexes. 1. Algorithms and Computers -- 1.1. Introduction -- 1.2. Computers -- 1.3. Software and Computer Languages -- 1.4. Data Structures -- 1.5. Programming Practice -- 1.6. Some Comments on R -- References -- 2. Computer Arithmetic -- 2.1. Introduction -- 2.2. Positional Number Systems -- 2.3. Fixed Point Arithmetic -- 2.4. Floating Point Representations -- 2.5. Living with Floating Point Inaccuracies -- 2.6. The Pale and Beyond -- 2.7. Conditioned Problems and Stable Algorithms -- Programs and Demonstrations -- Exercises -- References -- 3. Matrices and Linear Equations -- 3.1. Introduction -- 3.2. Matrix Operations -- 3.3. Solving Triangular Systems -- 3.4. Gaussian Elimination -- 3.5. Cholesky Decomposition -- 3.6. Matrix Norms -- 3.7. Accuracy and Conditioning -- 3.8. Matrix Computations in R -- Programs and Demonstrations -- Exercises -- References. 4. More Methods for Solving Linear Equations -- 4.1. Introduction -- 4.2. Full Elimination with Complete Pivoting -- 4.3. Banded Matrices -- 4.4. Applications to ARMA Time-Series Models -- 4.5. Toeplitz Systems -- 4.6. Sparse Matrices -- 4.7. Iterative Methods -- 4.8. Linear Programming -- Programs and Demonstrations -- Exercises -- References -- 5. Regression Computations -- 5.1. Introduction -- 5.2. Condition of the Regression Problem -- 5.3. Solving the Normal Equations -- 5.4. Gram-Schmidt Orthogonalization -- 5.5. Householder Transformations -- 5.6. Householder Transformations for Least Squares -- 5.7. Givens Transformations -- 5.8. Givens Transformations for Least Squares -- 5.9. Regression Diagnostics -- 5.10. Hypothesis Tests -- 5.11. Conjugate Gradient Methods -- 5.12. Doolittle, the Sweep, and All Possible Regressions -- 5.13. Alternatives to Least Squares -- 5.14. Comments -- Programs and Demonstrations -- Exercises -- References. 6. Eigenproblems -- 6.1. Introduction -- 6.2. Theory -- 6.3. Power Methods -- 6.4. The Symmetric Eigenproblem and Tridiagonalization -- 6.5. The QR Algorithm -- 6.6. Singular Value Decomposition -- 6.7. Applications -- 6.8. Complex Singular Value Decomposition -- Programs and Demonstrations -- Exercises -- References -- 7. Functions: Interpolation, Smoothing, and Approximation -- 7.1. Introduction -- 7.2. Interpolation -- 7.3. Interpolating Splines -- 7.4. Curve Fitting with Splines: Smoothing and Regression -- 7.5. Mathematical Approximation -- 7.6. Practical Approximation Techniques -- 7.7. Computing Probability Functions -- Programs and Demonstrations -- Exercises -- References -- 8. Introduction to Optimization and Nonlinear Equations -- 8.1. Introduction -- 8.2. Safe Univariate Methods: Lattice Search, Golden Section, and Bisection -- 8.3. Root Finding -- 8.4. First Digression: Stopping and Condition. 8.5. Multivariate Newton's Methods -- 8.6. Second Digression: Numerical Differentiation -- 8.7. Minimization and Nonlinear Equations -- 8.8. Condition and Scaling -- 8.9. Implementation -- 8.10. A Non-Newton Method: Nelder-Mead -- Programs and Demonstrations -- Exercises -- References -- 9. Maximum Likelihood and Nonlinear Regression -- 9.1. Introduction -- 9.2. Notation and Asymptotic Theory of Maximum Likelihood -- 9.3. Information, Scoring, and Variance Estimates -- 9.4. An Extended Example -- 9.5. Concentration, Iteration, and the EM Algorithm -- 9.6. Multiple Regression in the Context of Maximum Likelihood -- 9.7. Generalized Linear Models -- 9.8. Nonlinear Regression -- 9.9. Parameterizations and Constraints -- Programs and Demonstrations -- Exercises -- References -- 10. Numerical Integration and Monte Carlo Methods -- 10.1. Introduction -- 10.2. Motivating Problems -- 10.3. One-Dimensional Quadrature. 10.4. Numerical Integration in Two or More Variables -- 10.5. Uniform Pseudorandom Variables -- 10.6. Quasi-Monte Carlo Integration -- 10.7. Strategy and Tactics -- Programs and Demonstrations -- Exercises -- References -- 11. Generating Random Variables from Other Distributions -- 11.1. Introduction -- 11.2. General Methods for Continuous Distributions -- 11.3. Algorithms for Continuous Distributions -- 11.4. General Methods for Discrete Distributions -- 11.5. Algorithms for Discrete Distributions -- 11.6. Other Randomizations -- 11.7. Accuracy in Random Number Generation -- Programs and Demonstrations -- Exercises -- References -- 12. Statistical Methods for Integration and Monte Carlo -- 12.1. Introduction -- 12.2. Distribution and Density Estimation -- 12.3. Distributional Tests -- 12.4. Importance Sampling and Weighted Observations -- 12.5. Testing Importance Sampling Weights -- 12.6. Laplace Approximations. 12.7. Randomized Quadrature -- 12.8. Spherical-Radial Methods -- Programs and Demonstrations -- Exercises -- References -- 13. Markov Chain Monte Carlo Methods -- 13.1. Introduction -- 13.2. Markov Chains -- 13.3. Gibbs Sampling -- 13.4. Metropolis-Hastings Algorithm -- 13.5. Time-Series Analysis -- 13.6. Adaptive Acceptance/Rejection -- 13.7. Diagnostics -- Programs and Demonstrations -- Exercises -- References -- 14. Sorting and Fast Algorithms -- 14.1. Introduction -- 14.2. Divide and Conquer -- 14.3. Sorting Algorithms -- 14.4. Fast Order Statistics and Related Problems -- 14.5. Fast Fourier Transform -- 14.6. Convolutions and the Chirp-z Transform -- 14.7. Statistical Applications of the FFT -- 14.8. Combinatorial Problems -- Programs and Demonstrations -- Exercises -- References. Print version record. This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book offers a basic background in numerical analysis that emphasizes issues important to statisticians. The next several chapters cover a broad array of statistical tools, such as maximum likelihood and nonlinear regression. The author also treats the application of numerical tools; numerical integration and random number generation are explained in a unified manner reflecting complementary views of Monte Carlo methods. Each chapter contains exercises that range from simple questions to research problems. Most of the examples are accompanied by demonstration and source code available from the author's website. New in this second edition are demonstrations coded in R, as well as new sections on linear programming and the Nelder-Mead search algorithm. English. Mathematical statistics Data processing. http://id.loc.gov/authorities/subjects/sh85082137 Numerical analysis. http://id.loc.gov/authorities/subjects/sh85093237 Statistique mathématique Informatique. Analyse numérique. MATHEMATICS Probability & Statistics General. bisacsh Mathematical statistics Data processing fast Numerical analysis fast Electronic book. Electronic books. has work: Numerical methods of statistics (Text) https://id.oclc.org/worldcat/entity/E39PCGWTFhK7Pp6RRVRv4bkWCP https://id.oclc.org/worldcat/ontology/hasWork Print version: Monahan, John F. Numerical methods of statistics. 2nd ed. Cambridge ; New York : Cambridge University Press, ©2011 9780521191586 (DLC) 2011287063 (OCoLC)708741707 Cambridge series on statistical and probabilistic mathematics ; 32. http://id.loc.gov/authorities/names/n96064948 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=366155 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=366155 Volltext |
| spellingShingle | Monahan, John F. Numerical methods of statistics / Cambridge series on statistical and probabilistic mathematics ; Algorithms and Computers -- Introduction -- Computers -- Software and Computer Languages -- Data Structures -- Programming Practice -- Some Comments on R -- References -- Computer Arithmetic -- Positional Number Systems -- Fixed Point Arithmetic -- Floating Point Representations -- Living with Floating Point Inaccuracies -- The Pale and Beyond -- Conditioned Problems and Stable Algorithms -- Programs and Demonstrations -- Exercises -- Matrices and Linear Equations -- Matrix Operations -- Solving Triangular Systems -- Gaussian Elimination -- Cholesky Decomposition -- Matrix Norms -- Accuracy and Conditioning -- Matrix Computations in R -- References. More Methods for Solving Linear Equations -- Full Elimination with Complete Pivoting -- Banded Matrices -- Applications to ARMA Time-Series Models -- Toeplitz Systems -- Sparse Matrices -- Iterative Methods -- Linear Programming -- Regression Computations -- Condition of the Regression Problem -- Solving the Normal Equations -- Gram-Schmidt Orthogonalization -- Householder Transformations -- Householder Transformations for Least Squares -- Givens Transformations -- Givens Transformations for Least Squares -- Regression Diagnostics -- Hypothesis Tests -- Conjugate Gradient Methods -- Doolittle, the Sweep, and All Possible Regressions -- Alternatives to Least Squares -- Comments -- Eigenproblems -- Theory -- Power Methods -- The Symmetric Eigenproblem and Tridiagonalization -- The QR Algorithm -- Singular Value Decomposition -- Applications -- Complex Singular Value Decomposition -- Functions: Interpolation, Smoothing, and Approximation -- Interpolation -- Interpolating Splines -- Curve Fitting with Splines: Smoothing and Regression -- Mathematical Approximation -- Practical Approximation Techniques -- Computing Probability Functions -- Introduction to Optimization and Nonlinear Equations -- Safe Univariate Methods: Lattice Search, Golden Section, and Bisection -- Root Finding -- First Digression: Stopping and Condition. Multivariate Newton's Methods -- Second Digression: Numerical Differentiation -- Minimization and Nonlinear Equations -- Condition and Scaling -- Implementation -- A Non-Newton Method: Nelder-Mead -- Maximum Likelihood and Nonlinear Regression -- Notation and Asymptotic Theory of Maximum Likelihood -- Information, Scoring, and Variance Estimates -- An Extended Example -- Concentration, Iteration, and the EM Algorithm -- Multiple Regression in the Context of Maximum Likelihood -- Generalized Linear Models -- Nonlinear Regression -- Parameterizations and Constraints -- Numerical Integration and Monte Carlo Methods -- Motivating Problems -- One-Dimensional Quadrature. Numerical Integration in Two or More Variables -- Uniform Pseudorandom Variables -- Quasi-Monte Carlo Integration -- Strategy and Tactics -- Generating Random Variables from Other Distributions -- General Methods for Continuous Distributions -- Algorithms for Continuous Distributions -- General Methods for Discrete Distributions -- Algorithms for Discrete Distributions -- Other Randomizations -- Accuracy in Random Number Generation -- Statistical Methods for Integration and Monte Carlo -- Distribution and Density Estimation -- Distributional Tests -- Importance Sampling and Weighted Observations -- Testing Importance Sampling Weights -- Laplace Approximations. Randomized Quadrature -- Spherical-Radial Methods -- Markov Chain Monte Carlo Methods -- Markov Chains -- Gibbs Sampling -- Metropolis-Hastings Algorithm -- Time-Series Analysis -- Adaptive Acceptance/Rejection -- Diagnostics -- Sorting and Fast Algorithms -- Divide and Conquer -- Sorting Algorithms -- Fast Order Statistics and Related Problems -- Fast Fourier Transform -- Convolutions and the Chirp-z Transform -- Statistical Applications of the FFT -- Combinatorial Problems -- Mathematical statistics Data processing. http://id.loc.gov/authorities/subjects/sh85082137 Numerical analysis. http://id.loc.gov/authorities/subjects/sh85093237 Statistique mathématique Informatique. Analyse numérique. MATHEMATICS Probability & Statistics General. bisacsh Mathematical statistics Data processing fast Numerical analysis fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85082137 http://id.loc.gov/authorities/subjects/sh85093237 |
| title | Numerical methods of statistics / |
| title_alt | Algorithms and Computers -- Introduction -- Computers -- Software and Computer Languages -- Data Structures -- Programming Practice -- Some Comments on R -- References -- Computer Arithmetic -- Positional Number Systems -- Fixed Point Arithmetic -- Floating Point Representations -- Living with Floating Point Inaccuracies -- The Pale and Beyond -- Conditioned Problems and Stable Algorithms -- Programs and Demonstrations -- Exercises -- Matrices and Linear Equations -- Matrix Operations -- Solving Triangular Systems -- Gaussian Elimination -- Cholesky Decomposition -- Matrix Norms -- Accuracy and Conditioning -- Matrix Computations in R -- References. More Methods for Solving Linear Equations -- Full Elimination with Complete Pivoting -- Banded Matrices -- Applications to ARMA Time-Series Models -- Toeplitz Systems -- Sparse Matrices -- Iterative Methods -- Linear Programming -- Regression Computations -- Condition of the Regression Problem -- Solving the Normal Equations -- Gram-Schmidt Orthogonalization -- Householder Transformations -- Householder Transformations for Least Squares -- Givens Transformations -- Givens Transformations for Least Squares -- Regression Diagnostics -- Hypothesis Tests -- Conjugate Gradient Methods -- Doolittle, the Sweep, and All Possible Regressions -- Alternatives to Least Squares -- Comments -- Eigenproblems -- Theory -- Power Methods -- The Symmetric Eigenproblem and Tridiagonalization -- The QR Algorithm -- Singular Value Decomposition -- Applications -- Complex Singular Value Decomposition -- Functions: Interpolation, Smoothing, and Approximation -- Interpolation -- Interpolating Splines -- Curve Fitting with Splines: Smoothing and Regression -- Mathematical Approximation -- Practical Approximation Techniques -- Computing Probability Functions -- Introduction to Optimization and Nonlinear Equations -- Safe Univariate Methods: Lattice Search, Golden Section, and Bisection -- Root Finding -- First Digression: Stopping and Condition. Multivariate Newton's Methods -- Second Digression: Numerical Differentiation -- Minimization and Nonlinear Equations -- Condition and Scaling -- Implementation -- A Non-Newton Method: Nelder-Mead -- Maximum Likelihood and Nonlinear Regression -- Notation and Asymptotic Theory of Maximum Likelihood -- Information, Scoring, and Variance Estimates -- An Extended Example -- Concentration, Iteration, and the EM Algorithm -- Multiple Regression in the Context of Maximum Likelihood -- Generalized Linear Models -- Nonlinear Regression -- Parameterizations and Constraints -- Numerical Integration and Monte Carlo Methods -- Motivating Problems -- One-Dimensional Quadrature. Numerical Integration in Two or More Variables -- Uniform Pseudorandom Variables -- Quasi-Monte Carlo Integration -- Strategy and Tactics -- Generating Random Variables from Other Distributions -- General Methods for Continuous Distributions -- Algorithms for Continuous Distributions -- General Methods for Discrete Distributions -- Algorithms for Discrete Distributions -- Other Randomizations -- Accuracy in Random Number Generation -- Statistical Methods for Integration and Monte Carlo -- Distribution and Density Estimation -- Distributional Tests -- Importance Sampling and Weighted Observations -- Testing Importance Sampling Weights -- Laplace Approximations. Randomized Quadrature -- Spherical-Radial Methods -- Markov Chain Monte Carlo Methods -- Markov Chains -- Gibbs Sampling -- Metropolis-Hastings Algorithm -- Time-Series Analysis -- Adaptive Acceptance/Rejection -- Diagnostics -- Sorting and Fast Algorithms -- Divide and Conquer -- Sorting Algorithms -- Fast Order Statistics and Related Problems -- Fast Fourier Transform -- Convolutions and the Chirp-z Transform -- Statistical Applications of the FFT -- Combinatorial Problems -- |
| title_auth | Numerical methods of statistics / |
| title_exact_search | Numerical methods of statistics / |
| title_full | Numerical methods of statistics / John F. Monahan. |
| title_fullStr | Numerical methods of statistics / John F. Monahan. |
| title_full_unstemmed | Numerical methods of statistics / John F. Monahan. |
| title_short | Numerical methods of statistics / |
| title_sort | numerical methods of statistics |
| topic | Mathematical statistics Data processing. http://id.loc.gov/authorities/subjects/sh85082137 Numerical analysis. http://id.loc.gov/authorities/subjects/sh85093237 Statistique mathématique Informatique. Analyse numérique. MATHEMATICS Probability & Statistics General. bisacsh Mathematical statistics Data processing fast Numerical analysis fast |
| topic_facet | Mathematical statistics Data processing. Numerical analysis. Statistique mathématique Informatique. Analyse numérique. MATHEMATICS Probability & Statistics General. Mathematical statistics Data processing Numerical analysis Electronic book. Electronic books. |
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