Numerical analysis for statisticians:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1999
|
| Schriftenreihe: | Statistics and computing
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XV, 356 S. graph. Darst. |
| ISBN: | 0387949798 |
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| 245 | 1 | 0 | |a Numerical analysis for statisticians |c Kenneth Lange |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1999 | |
| 300 | |a XV, 356 S. |b graph. Darst. | ||
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| 650 | 4 | |a Statistique mathématique | |
| 650 | 7 | |a Statistique mathématique |2 ram | |
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Datensatz im Suchindex
| _version_ | 1804127273053323264 |
|---|---|
| adam_text | KENNETH LANGE NUMERICAL ANALYSIS FOR STATISTICIANS SPRINGER CONTENTS
PREFACE V 1 RECURRENCE RELATIONS 1 1.1 INTRODUCTION 1 1.2 BINOMIAL
COEFRCIENTS 1 1.3 NUMBER OF PARTITIONS OF A SET 2 1.4 HORNER S METHOD 2
1.5 SAMPLE MEANS AND VARIANCES 3 1.6 EXPECTED FAMILY SIZE 4 1.7
POISSON-BINOMIAL DISTRIBUTION 4 1.8 A MULTINOMIAL TEST STATISTIC 5 1.9
AN UNSTABLE RECURRENCE 6 1.10 QUICK SORT 7 1.11 PROBLEMS 9 REFERENCES 10
2 POWER SERIES EXPANSIONS 12 2.1 INTRODUCTION 12 2.2 EXPANSION OF P(S) N
13 2.2.1 APPLICATION TO MOMENTS 13 2.3 EXPANSION OF E P W 14 2.3.1
MOMENTS TO CUMULANTS AND VICE VERSA 14 2.3.2 COMPOUND POISSON
DISTRIBUTIONS 14 2.3.3 EVALUATION OF HERMITE POLYNOMIALS 15 2.4 STANDARD
NORMAL DISTRIBUTION FUNCTION 15 X CONTENTS 2.5 INCOMPLETE GAMMA FUNCTION
16 2.6 INCOMPLETE BETA FUNCTION 17 2.7 CONNECTIONS TO OTHER
DISTRIBUTIONS 18 2.7.1 CHI-SQUARE AND STANDARD NORMAL 18 2.7.2 POISSON
18 2.7.3 BINOMIAL AND NEGATIVE BINOMIAL 18 2.7.4 F AND STUDENT S T 19
2.7.5 MONOTONIE TRANSFORMATIONS 20 2.8 PROBLEMS 21 REFERENCES 24 3
CONTINUED FRACTION EXPANSIONS 25 3.1 INTRODUCTION 25 3.2 WALLIS S
ALGORITHM 27 3.3 EQUIVALENCE TRANSFORMATIONS 27 3.4 GAUSS S EXPANSION OF
HYPERGEOMETRIC FUNCTIONS 29 3.5 EXPANSION OF THE INCOMPLETE GAMMA
FUNCTION 31 3.6 PROBLEMS 33 REFERENCES 35 4 ASYMPTOTIC EXPANSIONS 37 4.1
INTRODUCTION 37 4.2 ORDER RELATIONS 38 4.3 FINITE TAYLOR EXPANSIONS 39
4.4 EXPANSIONS VIA INTEGRATION BY PARTS 42 4.4.1 EXPONENTIAL INTEGRAL 42
4.4.2 INCOMPLETE GAMMA FUNCTION 43 4.4.3 LAPLACE TRANSFORMS 44 4.5
GENERAL DEFINITION OF AN ASYMPTOTIC EXPANSION 44 4.6 LAPLACE S METHOD 44
4.6.1 MOMENTS OF AN ORDER STATISTIC 45 4.6.2 STIRLING S FORMULA 47 4.6.3
POSTERIOR EXPECTATIONS 47 4.7 VALIDATION OF LAPLACE S METHOD 48 4.8
PROBLEMS 49 REFERENCES 51 5 SOLUTION OF NONLINEAR EQUATIONS 53 5.1
INTRODUCTION 53 5.2 BISECTION 53 5.2.1 COMPUTATION OF QUANTILES BY
BISECTION . 54 5.2.2 SHORTEST XUEONFIDENCE INTERVAL 55 5.3 FUNCTIONAL
ITERATION 57 5.3.1 FRACTIONAL LINEAR TRANSFORMATIONS 58 5.3.2 EXTINCTION
PROBABILITIES BY FUNCTIONAL ITERATION . . 59 CONTENTS XI 5.4 NEWTON S
METHOD 61 5.4.1 DIVISION WITHOUT DIVIDING 63 5.4.2 EXTINCTION
PROBABILITIES BY NEWTON S METHOD ... 63 5.5 PROBLEMS 65 REFERENCES 67 6
VECTOR AND MATRIX NORMS 68 6.1 INTRODUCTION 68 6.2 ELEMENTARY PROPERTIES
OF VECTOR NORMS 68 6.3 ELEMENTARY PROPERTIES OF MATRIX NORMS 70 6.4
ITERATIVE SOLUTION OF LINEAR EQUATIONS 73 6.4.1 JACOBI S METHOD 74 6.4.2
PAN AND REIF S ITERATION SCHEME 74 6.4.3 EQUILIBRIUM DISTRIBUTION OF A
MARKOV CHAIN .... 74 6.5 CONDITION NUMBER OF A MATRIX 75 6.6 PROBLEMS 77
REFERENCES 78 7 LINEAR REGRESSION AND MATRIX INVERSION 79 7.1
INTRODUCTION 79 7.2 MOTIVATION FROM LINEAR REGRESSION 80 7.3 MOTIVATION
FROM MULTIVARIATE ANALYSIS 80 7.4 DEFINITION OF THE SWEEP OPERATOR 81
7.5 PROPERTIES OF THE SWEEP OPERATOR 82 7.6 APPLICATIONS OF SWEEPING 84
7.7 GRAM-SCHMIDT ORTHOGONALIZATION 85 7.8 WOODBURY S FORMULA 86 7.9
PROBLEMS 87 REFERENCES 90 8 EIGENVALUES AND EIGENVECTORS 92 8.1
INTRODUCTION 92 8.2 JACOBI S METHOD 93 8.3 THE RAYLEIGH QUOTIENT 98 8.4
PROBLEMS 100 REFERENCES 102 9 SPLINES 103 9.1 INTRODUCTION 103 9.2
DEFINITION AND BASIC PROPERTIES 104 9.3 APPLICATIONS TO DIFFERENTIATION
AND INTEGRATION 108 9.4 APPLICATION TO NONPARAMETRIC REGRESSION 109 9.5
PROBLEMS 112 REFERENCES 114 XII CONTENTS 10 THE EM ALGORITHM 115 10.1
INTRODUCTION 115 10.2 GENERAL DEFINITION OF THE EM ALGORITHM 116 10.3
ASCENT PROPERTY OF THE EM ALGORITHM 117 10.3.1 TECHNICAL NOTE 119 10.4
ALLELE FREQUENCY ESTIMATION 119 10.5 TRANSMISSION TOMOGRAPHY 122 10.6
PROBLEMS 125 REFERENCES 129 11 NEWTON S METHOD AND SCORING 130 11.1
INTRODUCTION 130 11.2 NEWTON S METHOD 130 11.3 SCORING 131 11.4
GENERALIZED LINEAR MODELS 134 11.5 THE GAUSS-NEWTON ALGORITHM 135 11.6
QUASI-NEWTON METHODS 136 11.7 PROBLEMS 138 REFERENCES 142 12 VARIATIONS
ON THE EM THEME 143 12.1 INTRODUCTION 143 12.2 ITERATIVE PROPORTIONAL
FITTING 143 12.3 EM GRADIENT ALGORITHM 145 12.3.1 APPLICATION TO THE
DIRICHLET DISTRIBUTION 146 12.4 BAYESIAN EM 147 12.5 ACCELERATED EM 147
12.6 EM ALGORITHMS WITHOUT MISSING DATA 149 12.6.1 QUADRATIC LOWER BOUND
PRINCIPLE 149 12.6.2 ELLIPTICALLY SYMMETRIE DENSITIES AND L P REGRESSION
150 12.6.3 TRANSMISSION TOMOGRAPHY REVISITED 151 12.7 PROBLEMS 153
REFERENCES 158 13 CONVERGENCE OF OPTIMIZATION ALGORITHMS 160 13.1
INTRODUCTION 160 13.2 CALCULUS PRELIMINARIES 161 13.3 LOCAL CONVERGENCE
162 13.4 GLOBAL CONVERGENCE 166 13.5 PROBLEMS 170 REFERENCES 175 14
CONSTRAINED OPTIMIZATION 177 14.1 INTRODUCTION 177 CONTENTS XIII 14.2
NECESSARY AND SUFFICIENT CONDITIONS FOR A MINIMUM .... 178 14.3
QUADRATIC PROGRAMMING WITH EQUALITY CONSTRAINTS .... 184 14.4 AN
ADAPTIVE BARRIER METHOD 185 14.5 STANDARD ERRORS 187 14.6 PROBLEMS 188
REFERENCES 190 15 CONCRETE HUBERT SPACES 191 15.1 INTRODUCTION 191 15.2
DEFINITIONS AND BASIC PROPERTIES 191 15.3 FOURIER SERIES 194 15.4
ORTHOGONAL POLYNOMIALS 197 15.5 PROBLEMS 204 REFERENCES 206 16
QUADRATURE METHODS 207 16.1 INTRODUCTION 207 16.2 EULER-MACLAURIN SUM
FORMULA 208 16.3 ROMBERG S ALGORITHM 210 16.4 ADAPTIVE QUADRATURE 213
16.5 TAMING BAD INTEGRANDS 213 16.6 GAUSSIAN QUADRATURE 214 16.7
PROBLEMS 217 REFERENCES 219 17 THE FOURIER TRANSFORM 221 17.1
INTRODUCTION 221 17.2 BASIC PROPERTIES 222 17.3 EXAMPLES 223 17.4
FURTHER THEORY 225 17.5 EDGEWORTH EXPANSIONS 229 17.6 PROBLEMS . 233
REFERENCES 234 18 THE FINITE FOURIER TRANSFORM 235 18.1 INTRODUCTION 235
18.2 BASIC PROPERTIES 236 18.3 DERIVATION OF THE FAST FOURIER TRANSFORM
237 18.4 APPROXIMATION OF FOURIER SERIES COEFFICIENTS 238 18.5
CONVOLUTION 242 18.6 TIME SERIES 245 18.7 PROBLEMS 247 REFERENCES 250
XIV CONTENTS 19 WAVELETS 252 19.1 INTRODUCTION 252 19.2 HAAR S WAVELETS
253 19.3 HISTOGRAM ESTIMATORS 255 19.4 DAUBECHIES WAVELETS 256 19.5
MULTIRESOLUTION ANALYSIS 262 19.6 IMAGE COMPRESSION AND THE FAST WAVELET
TRANSFORM . . . 263 19.7 PROBLEMS 265 REFERENCES 267 20 GENERATING
RANDOM DEVIATES 269 20.1 INTRODUCTION 269 20.2 THE INVERSE METHOD 270
20.3 NORMAL RANDOM DEVIATES 271 20.4 ACCEPTANCE-REJECTION METHOD 272
20.5 RATIO METHOD 277 20.6 DEVIATES BY DEFINITION 278 20.7 MULTIVARIATE
DEVIATES 279 20.8 PROBLEMS 281 REFERENCES 284 21 INDEPENDENT MONTE CARLO
286 21.1 INTRODUCTION 286 21.2 IMPORTANCE SAMPLING 287 21.3 STRATIFLED
SAMPLING 289 21.4 ANTITHETIC VARIATES 290 21.5 CONTROL VARIATES 291 21.6
RAO-BLACKWELLIZATION 292 21.7 EXACT TESTS OF INDEPENDENCE IN CONTINGENCY
TABLES .... 293 21.8 PROBLEMS 295 REFERENCES 297 22 BOOTSTRAP
CALCULATIONS 299 22.1 INTRODUCTION 299 22.2 RANGE OF APPLICATIONS 300
22.3 BALANCED BOOTSTRAP SIMULATIONS 305 22.4 ANTITHETIC BOOTSTRAP
SIMULATIONS 306 22.5 IMPORTANCE RESAMPLING 307 22.6 PROBLEMS 310
REFERENCES 312 23 FINITE-STATE MARKOV CHAMS 314 23.1 INTRODUCTION 314
23.2 DISCRETE-TIME MARKOV CHAMS 315 23.3 HIDDEN MARKOV CHAINS 318
CONTENTS XV 23.4 CONTINUOUS-TIME MARKOV CHAINS 321 23.5 CALCULATION OF
MATRIX EXPONENTIALS 324 23.6 PROBLEMS 325 REFERENCES 328 24 MARKOV CHAIN
MONTE CARLO 330 24.1 INTRODUCTION 330 24.2 THE HASTINGS-METROPOLIS
ALGORITHM 331 24.3 GIBBS SAMPLING 332 24.4 OTHER EXAMPLES OF
HASTINGS-METROPOLIS SAMPLING 334 24.5 SOME PRACTICAL ADVICE 336 24.6
CONVERGENCE OF THE INDEPENDENCE SAMPLER 337 24.7 SIMULATED ANNEALING 339
24.8 PROBLEMS 340 REFERENCES 342 INDEX 345
|
| any_adam_object | 1 |
| author | Lange, Kenneth 1946- |
| author_GND | (DE-588)142260576 |
| author_facet | Lange, Kenneth 1946- |
| author_role | aut |
| author_sort | Lange, Kenneth 1946- |
| author_variant | k l kl |
| building | Verbundindex |
| bvnumber | BV012618991 |
| callnumber-first | Q - Science |
| callnumber-label | QA297 |
| callnumber-raw | QA297.L34 1999 |
| callnumber-search | QA297.L34 1999 |
| callnumber-sort | QA 3297 L34 41999 |
| callnumber-subject | QA - Mathematics |
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| classification_tum | MAT 650f |
| ctrlnum | (OCoLC)38842134 (DE-599)BVBBV012618991 |
| dewey-full | 519.4 519.421 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.4 519.4 21 |
| dewey-search | 519.4 519.4 21 |
| dewey-sort | 3519.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV012618991 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:30:43Z |
| institution | BVB |
| isbn | 0387949798 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008571479 |
| oclc_num | 38842134 |
| open_access_boolean | |
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| physical | XV, 356 S. graph. Darst. |
| publishDate | 1999 |
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| publisher | Springer |
| record_format | marc |
| series2 | Statistics and computing |
| spelling | Lange, Kenneth 1946- Verfasser (DE-588)142260576 aut Numerical analysis for statisticians Kenneth Lange New York [u.a.] Springer 1999 XV, 356 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistics and computing Literaturangaben Analyse numérique Analyse numérique ram Computational statistics gtt MÉTODOS COMPUTACIONAIS (PESQUISA OPERACIONAL) larpcal Statistique mathématique Statistique mathématique ram Numerical analysis Mathematical statistics Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s Statistik (DE-588)4056995-0 s 1\p DE-604 DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008571479&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 | Lange, Kenneth 1946- Numerical analysis for statisticians Analyse numérique Analyse numérique ram Computational statistics gtt MÉTODOS COMPUTACIONAIS (PESQUISA OPERACIONAL) larpcal Statistique mathématique Statistique mathématique ram Numerical analysis Mathematical statistics Numerische Mathematik (DE-588)4042805-9 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4056995-0 |
| title | Numerical analysis for statisticians |
| title_auth | Numerical analysis for statisticians |
| title_exact_search | Numerical analysis for statisticians |
| title_full | Numerical analysis for statisticians Kenneth Lange |
| title_fullStr | Numerical analysis for statisticians Kenneth Lange |
| title_full_unstemmed | Numerical analysis for statisticians Kenneth Lange |
| title_short | Numerical analysis for statisticians |
| title_sort | numerical analysis for statisticians |
| topic | Analyse numérique Analyse numérique ram Computational statistics gtt MÉTODOS COMPUTACIONAIS (PESQUISA OPERACIONAL) larpcal Statistique mathématique Statistique mathématique ram Numerical analysis Mathematical statistics Numerische Mathematik (DE-588)4042805-9 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Analyse numérique Computational statistics MÉTODOS COMPUTACIONAIS (PESQUISA OPERACIONAL) Statistique mathématique Numerical analysis Mathematical statistics Numerische Mathematik Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008571479&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT langekenneth numericalanalysisforstatisticians |