Mathematical statistics: problems and detailed solutions
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
de Gruyter
1998
|
| Series: | De Gruyter textbook
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Erg. zu: Pestman, Wiebe R.: Mathematical statistics - an introduction |
| Physical Description: | IX, 325 S. graph. Darst. |
| ISBN: | 3110153580 3110153599 |
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MARC
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| 245 | 1 | 0 | |a Mathematical statistics |b problems and detailed solutions |c Wiebe R. Pestman ; Ivo B. Alberink |
| 264 | 1 | |a Berlin [u.a.] |b de Gruyter |c 1998 | |
| 300 | |a IX, 325 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804126550640033792 |
|---|---|
| adam_text | Table of contents
Chapter 1. Probability theory
1.1 Summary of Chapter I 1
1.1.1 Probability spaces 1
1.1.2 Stochastic variables 2
1.1.3 Product measures and statistical independence 2
1.1.4 Functions of stochastic vectors 3
1.1.5 Expectation, variance and covariance of stochastic variables 3
1.1.6 Statistical independence of normally distributed variables 4
1.1.7 Distribution functions and probability distributions 5
1.1.8 Moments, moment generating functions and characteristic functions 6
1.1.9 The central limit theorem 8
1.1.10 Transformation of probability densities 8
1.2 Exercises to Chapter I 8
Chapter 2. Statistics and their probability distributions,
estimation theory
2.1 Summary of Chapter II 49
2.1.1 Introduction 49
2.1.2 The gamma distribution and the x2 distribution 50
2.1.3 The t distribution 50
2.1.4 Statistics to measure differences in mean 51
2.1.5 The F distribution 51
2.1.6 The beta distribution 52
2.1.7 Populations which are not normally distributed 53
2.1.8 Bayesian estimation 53
2.1.9 Estimation theory in a more general framework 54
2.1.10 Maximum likelihood estimation, sufficiency 56
2.2 Exercises to Chapter II 56
Chapter 3. Hypothesis testing
3.1 Summary of Chapter III 110
3.1.1 The Neyman Pearson theory 110
viii Table of contents
3.1.2 Hypothesis tests concerning normally distributed populations 111
3.1.3 The x2 test on goodness of fit 113
3.1.4 The x2 test on statistical independence 113
3.2 Exercises to Chapter III 114
Chapter 4. Simple regression analysis
4.1 Summary of Chapter IV 144
4.1.1 The method of least squares 144
4.1.2 Construction of an unbiased estimator of a2 145
4.1.3 Normal regression analysis 145
4.1.4 Pearson s product moment correlation coefficient 146
4.1.5 The sum of squares of errors as a measure of the amount of
linear structure 146
4.2 Exercises to Chapter IV 147
Chapter 5. Normal analysis of variance
5.1 Summary of Chapter V 165
5.1.1 One way analysis of variance 165
5.1.2 Two way analysis of variance 166
5.2 Exercises to Chapter V 167
Chapter 6. Non parametric methods
6.1 Summary of Chapter VI 176
6.1.1 The sign test, Wilcoxon s signed rank test 176
6.1.2 Wilcoxon s rank sum test 177
6.1.3 The runs test 177
6.1.4 Rank correlation tests 178
6.1.5 The Kruskal Wallis test 179
6.1.6 Friedman s test 179
6.2 Exercises to Chapter VI 180
Chapter 7. Stochastic analysis and its applications
in statistics
7.1 Summary of Chapter VII 201
7.1.1 The empirical distribution function associated with a sample 201
ix
7.1.2 Convergence of stochastic variables 201
7.1.3 The Glivenko Cantelli theorem 203
7.1.4 The Kolmogorov Smirnov test statistic 203
7.1.5 Metrics on the set of distribution functions 203
7.1.6 Smoothing techniques 204
7.1.7 Robustness of statistics 205
7.1.8 Trimmed means, the median and their robustness 205
7.1.9 Statistical functionals 206
7.1.10 The von Mises derivative; influence functions 209
7.1.11 Bootstrap methods 210
7.1.12 Estimation of densities by means of kernel densities 212
7.1.13 Estimation of densities by means of histograms 213
7.2 Exercises to Chapter VII 213
Chapter 8. Vectorial statistics
8.1 Summary of Chapter VIII 268
8.1.1 Linear algebra 268
8.1.2 The expectation vector and the covariance operator of
stochastic vectors 269
8.1.3 Vectorial samples 271
8.1.4 The vectorial normal distribution 271
8.1.5 Conditional probability distributions that emanate from
Gaussian ones 272
8.1.6 Vectorial samples from Gaussian distributed populations 273
8.1.7 Vectorial versions of the fundamental limit theorems 274
8.1.8 Normal correlation analysis 275
8.1.9 Multiple regression analysis 276
8.1.10 The multiple correlation coefficient 277
8.1.11 Exercises to Chapter VIII 278
Statistical tables 307
|
| any_adam_object | 1 |
| author | Pestman, Wiebe R. 1954- Alberink, Ivo B. 1971- |
| author_GND | (DE-588)173223176 (DE-588)173223184 |
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| author_role | aut aut |
| author_sort | Pestman, Wiebe R. 1954- |
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| building | Verbundindex |
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| dewey-full | 519.5/07621 519.5/076 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/076 21 519.5/076 |
| dewey-search | 519.5/076 21 519.5/076 |
| dewey-sort | 3519.5 276 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:19:14Z |
| institution | BVB |
| isbn | 3110153580 3110153599 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008088953 |
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| spelling | Pestman, Wiebe R. 1954- Verfasser (DE-588)173223176 aut Mathematical statistics problems and detailed solutions Wiebe R. Pestman ; Ivo B. Alberink Berlin [u.a.] de Gruyter 1998 IX, 325 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier De Gruyter textbook Erg. zu: Pestman, Wiebe R.: Mathematical statistics - an introduction Inferência estatística (problemas e exercícios) larpcal Inferência paramétrica (problemas e exercícios) larpcal Statistiek gtt Statistik Mathematical statistics -- Problems, exercises, etc Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Statistik (DE-588)4056995-0 s DE-604 Alberink, Ivo B. 1971- Verfasser (DE-588)173223184 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008088953&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pestman, Wiebe R. 1954- Alberink, Ivo B. 1971- Mathematical statistics problems and detailed solutions Inferência estatística (problemas e exercícios) larpcal Inferência paramétrica (problemas e exercícios) larpcal Statistiek gtt Statistik Mathematical statistics -- Problems, exercises, etc Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4143389-0 |
| title | Mathematical statistics problems and detailed solutions |
| title_auth | Mathematical statistics problems and detailed solutions |
| title_exact_search | Mathematical statistics problems and detailed solutions |
| title_full | Mathematical statistics problems and detailed solutions Wiebe R. Pestman ; Ivo B. Alberink |
| title_fullStr | Mathematical statistics problems and detailed solutions Wiebe R. Pestman ; Ivo B. Alberink |
| title_full_unstemmed | Mathematical statistics problems and detailed solutions Wiebe R. Pestman ; Ivo B. Alberink |
| title_short | Mathematical statistics |
| title_sort | mathematical statistics problems and detailed solutions |
| title_sub | problems and detailed solutions |
| topic | Inferência estatística (problemas e exercícios) larpcal Inferência paramétrica (problemas e exercícios) larpcal Statistiek gtt Statistik Mathematical statistics -- Problems, exercises, etc Statistik (DE-588)4056995-0 gnd |
| topic_facet | Inferência estatística (problemas e exercícios) Inferência paramétrica (problemas e exercícios) Statistiek Statistik Mathematical statistics -- Problems, exercises, etc Aufgabensammlung |
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