Unbiased estimators and their applications: 2 Multivariate case
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Dordrecht u.a.
Kluwer Acad. Publ.
1996
|
| Series: | Mathematics and its applications
362 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 262 S. |
| ISBN: | 0792339398 |
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MARC
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| 245 | 1 | 0 | |a Unbiased estimators and their applications |n 2 |p Multivariate case |c by V. G. Voinov and M. S. Nikulin |
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| adam_text | Contents
Preface vii
Chapter I. Basic Remarks on Multivariate Probability Distributions
1. Cumulative Distribution Function and Probability Density Function . 1
2. Marginal and Conditional Distributions. Independence 3
3. Expected Values and Moments 5
4. Characteristic Functions 12
5. Multivariate Normal Distribution 14
6. Some Multivariate Discrete Distributions 22
7. Examples of Continuous Multivariate Distributions 30
Chapter II. Elements of the Theory of Point Statistical Estimation
in the Multivariate Case
1. Samples, Statistics, Estimators and Problems of
Statistical Estimation 43
2. Risk of Statistical Estimator. Consistency. Unbiasedness 46
3. Sufficiency, Completeness and Unbiased Estimators 48
4. The Rao Cramer Inequality 51
5. The Rao Blackwell Kolmogorov Theorem 60
6. On Estimating Parameters of the Multivariate Normal Distribution . 62
7. The Stein Approach for Estimators Improvement 74
Chapter III. Techniques for Constructing Unbiased Estimators
1. Techniques for Constructing MVUEs 96
2. Unbiased Estimators for the Multivariate
Probability Density Functions 110
3. Minimum Variance Unbiased Estimation for Multivariate Modified
Power Series Distributions 124
Chapter XV. Applications of Unbiased Estimators
1. On an Estimating the Momentum of a Relativistic Particle 137
2. A Statistical Group Classification of Normal Populations 140
3. A Remark on the Chauvenet Criterion 151
4. Testing Hypotheses for Small Samples in the Presence of
Sufficient Statistics 155
5. A Remark on Using of Conditional Distributions. Gerig s Test 167
6. A Remark on Analysis of Variance 172
7. Unbiased estimators of the reliability 178
8. A Chi Square Goodness of Fit Test for
vi Contents
Several Exponentials With a Common Shift 185
Appendix 1. Tables of Unbiased Estimators
Al. MVUEs for Functions of Parameters of the
Multivariate Normal Distribution 191
A2. MVUEs for Functions of Parameters of the
Multinomial Distribution 202
A3. MVUEs for Functions of Parameters of the
Trinomial Distribution 204
A4. MVUEs for Functions of Parameters of the
Negative Multinomial Distribution 205
A5. MVUEs for the Left Truncated Multivariate Modified
Power Series Distribution 208
A6. MVUEs for Functions of Parameters of the Left Truncated
Multivariate Exponential Distribution ( r is known) 212
A7. MVUEs for Functions of Parameters of the Left Truncated
Multivariate Exponential Distribution 215
A8. MVUEs for a two dimensional one truncation parameter family .. 219
Appendix 2. On Evaluating Some Multivariable Integrals 222
Appendix 3. Partitions and Some Multivariable Statistical
Problems 228
References 241
Subject Index 252
Author Index 258
|
| any_adam_object | 1 |
| author | Voinov, Vasilij G. Nikulin, Michail S. |
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| author_facet | Voinov, Vasilij G. Nikulin, Michail S. |
| author_role | aut aut |
| author_sort | Voinov, Vasilij G. |
| author_variant | v g v vg vgv m s n ms msn |
| building | Verbundindex |
| bvnumber | BV010719607 |
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| id | DE-604.BV010719607 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:57:46Z |
| institution | BVB |
| isbn | 0792339398 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007158010 |
| oclc_num | 637397997 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-824 DE-83 |
| owner_facet | DE-12 DE-384 DE-824 DE-83 |
| physical | IX, 262 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Voinov, Vasilij G. Verfasser aut Nesmeščennye ocenki i ich primenenija Unbiased estimators and their applications 2 Multivariate case by V. G. Voinov and M. S. Nikulin Dordrecht u.a. Kluwer Acad. Publ. 1996 IX, 262 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 362 Mathematics and its applications ... Análisis multivariante Nikulin, Michail S. Verfasser (DE-588)131649515 aut (DE-604)BV008279748 2 Mathematics and its applications 362 (DE-604)BV008163334 362 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007158010&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Voinov, Vasilij G. Nikulin, Michail S. Unbiased estimators and their applications Mathematics and its applications Análisis multivariante |
| title | Unbiased estimators and their applications |
| title_alt | Nesmeščennye ocenki i ich primenenija |
| title_auth | Unbiased estimators and their applications |
| title_exact_search | Unbiased estimators and their applications |
| title_full | Unbiased estimators and their applications 2 Multivariate case by V. G. Voinov and M. S. Nikulin |
| title_fullStr | Unbiased estimators and their applications 2 Multivariate case by V. G. Voinov and M. S. Nikulin |
| title_full_unstemmed | Unbiased estimators and their applications 2 Multivariate case by V. G. Voinov and M. S. Nikulin |
| title_short | Unbiased estimators and their applications |
| title_sort | unbiased estimators and their applications multivariate case |
| topic | Análisis multivariante |
| topic_facet | Análisis multivariante |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007158010&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008279748 (DE-604)BV008163334 |
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