Numerical methods of statistics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2011
|
| Edition: | 2. ed. |
| Series: | Cambridge series in statistical and probabilistic mathematics
7 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 447 S. graph. Darst. |
| ISBN: | 9780521191586 9780521139519 |
Staff View
MARC
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| 245 | 1 | 0 | |a Numerical methods of statistics |c John F. Monahan |
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Record in the Search Index
| _version_ | 1804147980136087552 |
|---|---|
| adam_text | Contents
Preface to the Second Edition page xiii
Preface to the First Edition XV
i Algorithms and Computers 1
l.i Introduction 1
1.2 Computers 3
1.3 Software and Computer Languages 5
1.4 Data Structures 8
1.5 Programming Practice 9
1.6 Some Comments on R 10
References 12
2 Computer Arithmetic 13
2.1 Introduction 13
2.2 Positional Number Systems 14
2.3 Fixed Point Arithmetic 17
2.4 Floating Point Representations 20
2.5 Living with Floating Point Inaccuracies 23
2.6 The Pale and Beyond 28
2.7 Conditioned Problems and Stable Algorithms 32
Programs and Demonstrations 34
Exercises 35
References 38
3 Matrices and Linear Equations 40
3.1 Introduction 40
3.2 Matrix Operations 41
3.3 Solving Triangular Systems 43
3.4 Gaussian Elimination 44
3.5 Cholesky Decomposition 50
3.6 Matrix Norms 54
3.7 Accuracy and Conditioning 55
3.8 Matrix Computations in R 60
Programs and Demonstrations 61
Exercises 63
References 65
Vll
67
67
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150
Contents
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
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
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
ix
151
151
153
156
159
163
168
170
177
179
183
186
186
188
191
197
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211
213
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217
219
219
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226
228
230
236
237
242
246
251
252
255
257
257
258
264
Contents
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
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
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
Numerical Integration and Monte Carlo Methods
10.1 Introduction
10.2 Motivating Problems
10.3 One-Dimensional Quadrature
271
278
286
291
295
297
299
303
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304
308
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400
Contents
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
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
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
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
Contents xi
14 Sorting and Fast Algorithms 403
14.1 Introduction 403
14.2 Divide and Conquer 403
14.3 Sorting Algorithms 405
14.4 Fast Order Statistics and Related Problems 408
14.5 Fast Fourier Transform 409
14.6 Convolutions and the Chirp-z Transform 413
14.7 Statistical Applications of the FFT 415
14.8 Combinatorial Problems 425
Programs and Demonstrations 429
Exercises 433
References 436
A uthor Index 43 9
Subject Index 444
|
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| dewey-sort | 3519.50285512 |
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| discipline | Psychologie Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
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| spelling | Monahan, John F. Verfasser aut Numerical methods of statistics John F. Monahan 2. ed. Cambridge [u.a.] Cambridge Univ. Press 2011 XVI, 447 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge series in statistical and probabilistic mathematics 7 Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Statistik (DE-588)4056995-0 s Numerisches Verfahren (DE-588)4128130-5 s DE-188 Datenverarbeitung (DE-588)4011152-0 s 1\p DE-604 Cambridge series in statistical and probabilistic mathematics 7 (DE-604)BV011442366 7 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024158822&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Monahan, John F. Numerical methods of statistics Cambridge series in statistical and probabilistic mathematics Numerisches Verfahren (DE-588)4128130-5 gnd Datenverarbeitung (DE-588)4011152-0 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4011152-0 (DE-588)4056995-0 |
| title | Numerical methods of statistics |
| 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 | Numerisches Verfahren (DE-588)4128130-5 gnd Datenverarbeitung (DE-588)4011152-0 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Numerisches Verfahren Datenverarbeitung Statistik |
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