Statistical decision rules and optimal inference:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Society
1982
|
| Series: | Translations of mathematical monographs
53 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Russ. übers. |
| Physical Description: | VIII, 499 S. |
| ISBN: | 0821845020 |
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| 245 | 1 | 0 | |a Statistical decision rules and optimal inference |c by N. N. Čencov |
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Record in the Search Index
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| adam_text | TABLE OF CONTENTS
PREFACE vii
INTRODUCTION 1
1. Statistical problems and statistical decisions 1
2. Probability measures and conditional distributions 13
3. Smooth manifolds and their mappings 37
4. Category theory and geometry 50
CHAPTER I. THE FORMAL DECISION PROBLEM 65
5. The category of statistical decisions 65
6. Markov geometry of families of probability distributions 76
7. Geometry of dominated families of probability distributions 92
8. Invariant information characteristics 113
CHAPTER II. EQUIVARIANT DIFFERENTIAL GEOMETRY OF
A COLLECTION OF PROBABILITY DISTRIBUTIONS 127
9. Geometry of the simplex of probability distributions on a finite
algebra 127
10. Projective geometry of a collection of probability distributions 140
11. Invariant Riemannian metric on a manifold of probability distrib¬
utions 156
12. Geodesic mean of probability distributions 165
CHAPTER III. SMOOTH FAMILIES OF PROBABILITY DISTRIB¬
UTIONS AND THE INFORMATION INEQUALITY 185
13. Finite dimensional approximation of infinite dimensional mani¬
folds of probability distributions 185
14. Differentiable families of probability distributions 199
15. The information inequality 213
16. Continuously differentiable families of probability distributions 228
v
Vi CONTENTS
CHAPTER IV. GEOMETRY OF EXPONENT FAMILIES OF
PROBABILITY DISTRIBUTIONS 245
17. Convex functions and the Legendre transformation 245
18. Exponent families of probability distributions 262
19. Natural parametrization of exponent families 279
20. Conjugate parametrizations of an exponent family of probability
distributions 290
21. Distributions of values of the directional statistic of an exponent
family and related families 303
22. Nonsymmetric Pythagorean geometry of the information devia¬
tion 319
23. Charts of an exponent family of probability distributions 334
CHAPTER V. OPTIMAL DECISION RULES IN THE EQUIV
ARIANT PROBLEM OF POINT ESTIMATION 355
24. Estimation of the unknown mean of a multivariate normal dis¬
tribution 355
25. Estimation of the unknown density of a probability
distribution 370
26. Invariant loss functions in problems of mathematical statistics 391
27. Optimal estimators for smooth families of probability distribu¬
tions 403
28. Quasi homogeneous families of probability distributions 437
APPENDIX 451
29. Random probability measures 451
NOTES AND COMMENTS 465
BIBLIOGRAPHY 477
INDEX 495
|
| any_adam_object | 1 |
| author | Čencov, Nikolaj Nikolaevič 1930-1992 |
| author_GND | (DE-588)172477654 |
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| author_sort | Čencov, Nikolaj Nikolaevič 1930-1992 |
| author_variant | n n č nn nnč |
| building | Verbundindex |
| bvnumber | BV000157038 |
| classification_rvk | SK 830 SK 835 |
| ctrlnum | (OCoLC)472094671 (DE-599)BVBBV000157038 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000157038 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:09:33Z |
| institution | BVB |
| isbn | 0821845020 |
| language | English |
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| physical | VIII, 499 S. |
| psigel | TUB-nveb |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Čencov, Nikolaj Nikolaevič 1930-1992 Verfasser (DE-588)172477654 aut Statističeskie rešajuščie pravila i optimal'nye vyvody Statistical decision rules and optimal inference by N. N. Čencov Providence, R.I. American Mathematical Society 1982 VIII, 499 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 53 Aus d. Russ. übers. Statistische Entscheidungsregel (DE-588)4182957-8 gnd rswk-swf Statistische Entscheidungstheorie (DE-588)4077850-2 gnd rswk-swf Entscheidungstheorie (DE-588)4138606-1 gnd rswk-swf Statistische Entscheidungsregel (DE-588)4182957-8 s DE-604 Entscheidungstheorie (DE-588)4138606-1 s Statistische Entscheidungstheorie (DE-588)4077850-2 s Translations of mathematical monographs 53 (DE-604)BV000002394 53 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000088537&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Čencov, Nikolaj Nikolaevič 1930-1992 Statistical decision rules and optimal inference Translations of mathematical monographs Statistische Entscheidungsregel (DE-588)4182957-8 gnd Statistische Entscheidungstheorie (DE-588)4077850-2 gnd Entscheidungstheorie (DE-588)4138606-1 gnd |
| subject_GND | (DE-588)4182957-8 (DE-588)4077850-2 (DE-588)4138606-1 |
| title | Statistical decision rules and optimal inference |
| title_alt | Statističeskie rešajuščie pravila i optimal'nye vyvody |
| title_auth | Statistical decision rules and optimal inference |
| title_exact_search | Statistical decision rules and optimal inference |
| title_full | Statistical decision rules and optimal inference by N. N. Čencov |
| title_fullStr | Statistical decision rules and optimal inference by N. N. Čencov |
| title_full_unstemmed | Statistical decision rules and optimal inference by N. N. Čencov |
| title_short | Statistical decision rules and optimal inference |
| title_sort | statistical decision rules and optimal inference |
| topic | Statistische Entscheidungsregel (DE-588)4182957-8 gnd Statistische Entscheidungstheorie (DE-588)4077850-2 gnd Entscheidungstheorie (DE-588)4138606-1 gnd |
| topic_facet | Statistische Entscheidungsregel Statistische Entscheidungstheorie Entscheidungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000088537&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
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