Mathematical statistics: an introduction
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
de Gruyter
1998
|
| Series: | De Gruyter textbook
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Erg. bildet: Pestman, Wiebe R.: Mathematical statistics - problems and detailed solutions |
| Physical Description: | IX, 545 S. Ill., graph. Darst. |
| ISBN: | 3110153564 3110153572 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | Table of contents
Chapter I. Probability theory
1.1 Probability spaces 1
1.2 Stochastic variables 9
1.3 Product measures and statistical independence 13
1.4 Functions of stochastic vectors 18
1.5 Expectation, variance and covariance of stochastic variables 21
1.6 Independence of normally distributed variables 30
1.7 Distribution functions and probability distributions 37
1.8 Moments, moment generating functions and characteristic functions 40
1.9 The central limit theorem 47
1.10 Transformation of probability densities 51
1.11 Exercises 53
Chapter II. Statistics and their probability distributions,
estimation theory
II. 1 Introduction 62
11.2 The gamma distribution and the ^ distribution 66
11.3 The t distribution 76
11.4 Statistics to measure differences in mean 80
11.5 The F distribution 86
11.6 The beta distribution 90
II. 7 Populations which are not normally distributed 95
11.8 Bayesian estimation 97
11.9 Estimation theory in a more general framework 103
11.10 Maximum likelihood estimation, sufficiency 119
11.11 Exercises 129
Chapter III. Hypothesis tests
111.1 The Neyman Pearson theory 142
111.2 Hypothesis tests concerning normally distributed populations 153
111.3 The x2 test on goodness of fit 165
viii Table of contents
111.4 The x2 test on statistical independence 171
111.5 Exercises 176
Chapter IV. Simple regression analysis
IV. 1 The method of least squares 182
IV.2 Construction of an unbiased estimator of a2 192
IV.3 Normal regression analysis 194
IV.4 Pearson s product moment correlation coefficient 198
IV. 5 The sum of squares of errors as a measure of the amount of
linear structure 201
IV.6 Exercises 204
Chapter V. Normal analysis of variance
V.I One way analysis of variance 208
V.2 Two way analysis of variance 214
V.3 Exercises 223
Chapter VI. Non parametric methods
VI. 1 The sign test, Wilcoxon s signed rank test 227
VI.2 Wilcoxon s rank sum test 233
VI.3 The runs test 238
VI.4 Rank correlation tests 241
VI.5 The Kruskal Wallis test 246
VI.6 Friedman s test 249
VI.7 Exercises 253
Chapter VII. Stochastic analysis and its applications
in statistics
VII. 1 The empirical distribution function associated with a sample 257
VII.2 Convergence of stochastic variables 259
VII.3 The Glivenko Cantelli theorem 276
VII.4 The Kolmogorov Smirnov test statistic 284
VII.5 Metrics on the set of distribution functions 288
VII.6 Smoothing techniques 299
VII.7 Robustness of statistics 305
ix
VII.8 Trimmed means, the median, and their robustness 311
VII.9 Statistical functionals 326
VII. 10 The von Mises derivative; influence functions 339
VII.ll Bootstrap methods 350
VII.12 Estimation of densities by means of kernel densities 357
VII.13 Estimation of densities by means of histograms 365
VII.14 Exercises 369
Chapter VIII. Vectorial statistics
VIII.l Linear algebra 382
VIII.2 The expectation vector and the covariance operator of
stochastic vectors 396
VIII.3 Vectorial samples 407
VIII.4 The vectorial normal distribution 410
VIII.5 Conditional probability distributions that emanate from
Gaussian ones 422
VIII.6 Vectorial samples from Gaussian distributed populations 428
VIII.7 Vectorial versions of the fundamental limit theorems 442
VIII.8 Normal correlation analysis 452
VIII.9 Multiple regression analysis 460
VIII. 10 The multiple correlation coefficient 471
VIII. 11 Exercises 477
Appendix A. Lebesgue s convergence theorems 482
Appendix B. Product measures 485
Appendix C. Conditional probabilities 488
Appendix D. The characteristic function of the Cauchy distribution 492
Appendix E. Metric spaces, equicontinuity 495
Appendix F. The Fourier transform and the existence of stoutly
tailed distribution functions 504
List of elementary probability densities 510
Frequently used symbols 512
Statistical tables 518
References 537
Index 541
|
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| author | Pestman, Wiebe R. 1954- |
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| dewey-full | 519.521 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 21 519.5 |
| dewey-search | 519.5 21 519.5 |
| dewey-sort | 3519.5 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| language | English |
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| spelling | Pestman, Wiebe R. 1954- Verfasser (DE-588)173223176 aut Mathematical statistics an introduction Wiebe R. Pestman Berlin [u.a.] de Gruyter 1998 IX, 545 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier De Gruyter textbook Erg. bildet: Pestman, Wiebe R.: Mathematical statistics - problems and detailed solutions Statistiek gtt Statistik Mathematical statistics Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content (DE-588)4123623-3 Lehrbuch gnd-content Statistik (DE-588)4056995-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008088957&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pestman, Wiebe R. 1954- Mathematical statistics an introduction Statistiek gtt Statistik Mathematical statistics Statistik (DE-588)4056995-0 gnd |
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| title | Mathematical statistics an introduction |
| title_auth | Mathematical statistics an introduction |
| title_exact_search | Mathematical statistics an introduction |
| title_full | Mathematical statistics an introduction Wiebe R. Pestman |
| title_fullStr | Mathematical statistics an introduction Wiebe R. Pestman |
| title_full_unstemmed | Mathematical statistics an introduction Wiebe R. Pestman |
| title_short | Mathematical statistics |
| title_sort | mathematical statistics an introduction |
| title_sub | an introduction |
| topic | Statistiek gtt Statistik Mathematical statistics Statistik (DE-588)4056995-0 gnd |
| topic_facet | Statistiek Statistik Mathematical statistics Einführung Lehrbuch |
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