Lectures in mathematical statistics: parts 1 and 2
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2005
|
| Series: | Translations of mathematical monographs
229 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 321 S. Illustrationen |
| ISBN: | 082183732X |
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Record in the Search Index
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| adam_text | Titel: Lectures in mathematical statistics
Autor: Lin kov, Ju. N.
Jahr: 2005
Contents
Foreword to the English Translation vii
Part 1 1
Preface to Part 1 3
Chapter 1. Samples from One-Dimensional Distributions 5
1.1. Empirical distribution function and its asymptotic behavior 5
1.2. Sample characteristics and their properties ¦ 8
1.3. Order statistics and their properties 13
1.4. The distributions of some functions of Gaussian random vectors 20
Chapter 2. Samples from Multidimensional Distributions 25
2.1. Empirical distribution function, sampling moments, and their
properties 25
2.2. Sampling regression and its properties 31
Chapter 3. Estimation of Unknown Parameters of Distributions 39
3.1. Statistical estimators and their quality measures 39
3.2. Estimation of a location parameter 49
3.3. Estimation of a scale parameter 56
3.4. The Cramér-Rao inequality and efficient estimators 61
3.5. The Cramér-Rao inequality for a multidimensional parameter 80
3.6. Integral inequalities of Cramér-Rao type 88
Chapter 4. Sufficient Statistics 99
4.1. Sufficient statistics and a theorem on factorization 99
4.2. Sufficient statistics and optimal estimators 113
Chapter 5. General Methods for Constructing Estimators 131
5.1. Method of moments 131
5.2. The maximum likelihood method 133
5.3. Bayes and minimax methods 142
5.4. Confidence intervals and regions 147
References to Part 1 153
vi CONTENTS
Part 2 155
Preface to Part 2 157
Chapter 1. General Theory of Hypotheses Testing 159
1.1. Testing two simple hypotheses 159
1.2. Distinguishing a finite number of simple hypotheses 173
1.3. Distinguishing composite hypotheses 182
Chapter 2. Asymptotic Distinguishability of Simple Hypotheses 203
2.1. Statistical hypotheses and tests 203
2.2. Types of the asymptotic distinguishability of families of hypothe-
ses. The characterization of types 205
2.3. Complete asymptotic distinguishability under the strong law of
large numbers 218
2.4. Complete asymptotic distinguishability under the weak conver-
gence 238
2.5. Contiguous families of hypotheses 248
Chapter 3. Goodness-of-Fit Tests 263
3.1. The setting of the problem. Kolmogorov test 263
3.2. The Pearson test 266
3.3. Smirnov test 275
3.4. Other goodness-of-fit tests 282
Chapter 4. Sequential Tests 293
4.1. Bayes sequential tests of hypotheses 293
4.2. Wald sequential tests 300
4.3. The optimality of a sequential Wald test 310
References to Part 2 317
Index 319
|
| any_adam_object | 1 |
| author | Linʹkov, Jurij N. 1938- |
| author_GND | (DE-588)141097183 |
| author_facet | Linʹkov, Jurij N. 1938- |
| author_role | aut |
| author_sort | Linʹkov, Jurij N. 1938- |
| author_variant | j n l jn jnl |
| building | Verbundindex |
| bvnumber | BV025402984 |
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| ctrlnum | (OCoLC)254693667 (DE-599)BVBBV025402984 |
| 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 |
| format | Book |
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| illustrated | Illustrated |
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| institution | BVB |
| isbn | 082183732X |
| language | English |
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| physical | VII, 321 S. Illustrationen |
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| publisher | American Math. Soc. |
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| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Linʹkov, Jurij N. 1938- Verfasser (DE-588)141097183 aut Lekcii po matematičeskoj statistike Lectures in mathematical statistics parts 1 and 2 Yu. N. Lin'kov Providence, RI American Math. Soc. 2005 VII, 321 S. Illustrationen txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 229 Aus dem Russ. übers. Stichprobe (DE-588)4057502-0 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Statistischer Test (DE-588)4077852-6 gnd rswk-swf Stichprobe (DE-588)4057502-0 s DE-604 Statistik (DE-588)4056995-0 s Statistischer Test (DE-588)4077852-6 s Translations of mathematical monographs 229 (DE-604)BV000002394 229 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020025083&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Linʹkov, Jurij N. 1938- Lectures in mathematical statistics parts 1 and 2 Translations of mathematical monographs Stichprobe (DE-588)4057502-0 gnd Statistik (DE-588)4056995-0 gnd Statistischer Test (DE-588)4077852-6 gnd |
| subject_GND | (DE-588)4057502-0 (DE-588)4056995-0 (DE-588)4077852-6 |
| title | Lectures in mathematical statistics parts 1 and 2 |
| title_alt | Lekcii po matematičeskoj statistike |
| title_auth | Lectures in mathematical statistics parts 1 and 2 |
| title_exact_search | Lectures in mathematical statistics parts 1 and 2 |
| title_full | Lectures in mathematical statistics parts 1 and 2 Yu. N. Lin'kov |
| title_fullStr | Lectures in mathematical statistics parts 1 and 2 Yu. N. Lin'kov |
| title_full_unstemmed | Lectures in mathematical statistics parts 1 and 2 Yu. N. Lin'kov |
| title_short | Lectures in mathematical statistics |
| title_sort | lectures in mathematical statistics parts 1 and 2 |
| title_sub | parts 1 and 2 |
| topic | Stichprobe (DE-588)4057502-0 gnd Statistik (DE-588)4056995-0 gnd Statistischer Test (DE-588)4077852-6 gnd |
| topic_facet | Stichprobe Statistik Statistischer Test |
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