Mathematical theory of statistics: statistical experiments and asymptotic decision theory
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin, [u.a.]
de Gruyter
1985
|
| Series: | De Gruyter studies in mathematics
7 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 492 Seiten Illustrationen |
| ISBN: | 0899250289 3110102587 |
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MARC
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| 100 | 1 | |a Strasser, Helmut |d 1948- |0 (DE-588)1030420785 |4 aut | |
| 245 | 1 | 0 | |a Mathematical theory of statistics |b statistical experiments and asymptotic decision theory |c Helmut Strasser |
| 264 | 1 | |a Berlin, [u.a.] |b de Gruyter |c 1985 | |
| 300 | |a XII, 492 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
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Contents
Chapter 1: Basic Notions on Probability Measures
1. Decomposition of probability measures 1
2. Distances between probability measures 5
3. Topologies and cr fields on sets of probability measures 13
4. Separable sets of probability measures 17
5. Transforms of bounded Borel measures 21
6. Miscellaneous results 30
Chapter 2: Elementary Theory of Testing Hypotheses
7. Basic definitions 38
8. Neyman Pearson theory for binary experiments 42
9. Experiments with monotone likelihood ratios 47
10. The generalized lemma of Neyman Pearson 54
11. Exponential experiments of rank 1 55
12. Two sided testing for exponential experiments: Part 1 58
13. Two sided testing for exponential experiments: Part 2 63
Chapter 3: Binary Experiments
14. The error function 68
15. Comparison of binary experiments 74
16. Representation of experiment types 78
17. Concave functions and Mellin transforms 81
18. Contiguity of probability measures 85
Chapter 4: Sufficiency, Exhaustivity, and Randomizations
19. The idea of sufficiency 92
20. Pairwise sufficiency and the factorization theorem 93
21. Sufficiency and topology 97
22. Comparison of dominated experiments by testing problems 98
23. Exhaustivity 101
24. Randomization of experiments 105
25. Statistical isomorphism 109
X Contents
Chapter 5: Exponential Experiments
26. Basic facts 115
27. Conditional tests 119
28. Gaussian shifts with nuisance parameters 124
Chapter 6: More Theory of Testing
29. Complete classes of tests 131
30. Testing for Gaussian shifts 135
31. Reduction of testing problems by invariance 140
32. The theorem of Hunt and Stein 147
Chapter 7: Theory of estimation
33. Basic notions of estimation 155
34. Median unbiased estimation for Gaussian shifts 162
35. Mean unbiased estimation 166
36. Estimation by desintegration 172
37. Generalized Bayes estimates 181
38. Full shift experiments and the convolution theorem 186
39. The structure model 200
40. Admissibility of estimators 215
Chapter 8: General decision theory
41. Experiments and their L spaces 227
42. Decision functions 230
43. Lower semicontinuity 234
44. Risk functions 237
45. A general minimax theorem 238
46. The minimax theorem of decision theory 240
47. Bayes solutions and the complete class theorem 242
48. The generalized theorem of Hunt and Stein 245
Chapter 9: Comparison of experiments
49. Basic concepts 257
50. Standard decision problems 262
51. Comparison of experiments by standard decision problems 264
52. Concave function criteria 266
53. Hellinger transforms and standard measures 270
Contents XI
54. Comparison of experiments by testing problems 273
55. The randomization criterion 278
56. Conical measures 287
57. Representation of experiments 288
58. Transformation groups and invariance 293
59. Topological spaces of experiments 296
Chapter 10: Asymptotic decision theory
60. Weakly convergent sequences of experiments 302
61. Contiguous sequences of experiments 305
62. Convergence in distribution of decision functions 308
63. Stochastic convergence of decision functions 312
64. Convergence of minimum estimates 317
65. Uniformly integrable experiments 324
66. Uniform tightness of generalized Bayes estimates 331
67. Convergence of generalized Bayes estimates 333
Chapter 11: Gaussian shifts on Hilbert spaces
68. Linear stochastic processes and cylinder set measures 340
69. Gaussian shift experiments 343
70. Banach sample spaces 350
71. Testing for Gaussian shifts 357
72. Estimation for Gaussian shifts 362
73. Testing and estimation for Banach sample spaces 372
Chapter 12: Differentiability and asymptotic expansions
74. Stochastic expansion of likelihood ratios 378
75. Differentiable curves 383
76. Differentiable experiments 387
77. Conditions for differentiability 390
78. Examples of differentiable experiments 395
79. The stochastic expansion of a differentiable experiment 402
Chapter 13: Asymptotic normality
80. Asymptotic normality 409
81. Exponential approximation and asymptotic sufficiency 419
82. Application to testing hypotheses 426
XII Contents
83. Application to estimation 437
84. Characterization of central sequences 446
Appendix: Notation and terminology 461
References 478
List of symbols 483
Author index 485
Subject index 487 |
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| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| isbn | 0899250289 3110102587 |
| language | English |
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| physical | XII, 492 Seiten Illustrationen |
| publishDate | 1985 |
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| spelling | Strasser, Helmut 1948- (DE-588)1030420785 aut Mathematical theory of statistics statistical experiments and asymptotic decision theory Helmut Strasser Berlin, [u.a.] de Gruyter 1985 XII, 492 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics 7 Plan d'expérience Prise de décision (Statistique) Statistique mathématique Experimental design Mathematical statistics Statistical decision Statistische Entscheidungstheorie (DE-588)4077850-2 gnd rswk-swf Entscheidungstheorie (DE-588)4138606-1 gnd rswk-swf Asymptotische Statistik (DE-588)4203167-9 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Statistische Entscheidungstheorie (DE-588)4077850-2 s DE-604 Statistik (DE-588)4056995-0 s Asymptotische Statistik (DE-588)4203167-9 s Asymptotik (DE-588)4126634-1 s Entscheidungstheorie (DE-588)4138606-1 s Erscheint auch als Online-Ausgabe 978-3-11-085082-6 De Gruyter studies in mathematics 7 (DE-604)BV000005407 7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000296360&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Strasser, Helmut 1948- Mathematical theory of statistics statistical experiments and asymptotic decision theory De Gruyter studies in mathematics Plan d'expérience Prise de décision (Statistique) Statistique mathématique Experimental design Mathematical statistics Statistical decision Statistische Entscheidungstheorie (DE-588)4077850-2 gnd Entscheidungstheorie (DE-588)4138606-1 gnd Asymptotische Statistik (DE-588)4203167-9 gnd Asymptotik (DE-588)4126634-1 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4077850-2 (DE-588)4138606-1 (DE-588)4203167-9 (DE-588)4126634-1 (DE-588)4056995-0 (DE-588)4123623-3 |
| title | Mathematical theory of statistics statistical experiments and asymptotic decision theory |
| title_auth | Mathematical theory of statistics statistical experiments and asymptotic decision theory |
| title_exact_search | Mathematical theory of statistics statistical experiments and asymptotic decision theory |
| title_full | Mathematical theory of statistics statistical experiments and asymptotic decision theory Helmut Strasser |
| title_fullStr | Mathematical theory of statistics statistical experiments and asymptotic decision theory Helmut Strasser |
| title_full_unstemmed | Mathematical theory of statistics statistical experiments and asymptotic decision theory Helmut Strasser |
| title_short | Mathematical theory of statistics |
| title_sort | mathematical theory of statistics statistical experiments and asymptotic decision theory |
| title_sub | statistical experiments and asymptotic decision theory |
| topic | Plan d'expérience Prise de décision (Statistique) Statistique mathématique Experimental design Mathematical statistics Statistical decision Statistische Entscheidungstheorie (DE-588)4077850-2 gnd Entscheidungstheorie (DE-588)4138606-1 gnd Asymptotische Statistik (DE-588)4203167-9 gnd Asymptotik (DE-588)4126634-1 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Plan d'expérience Prise de décision (Statistique) Statistique mathématique Experimental design Mathematical statistics Statistical decision Statistische Entscheidungstheorie Entscheidungstheorie Asymptotische Statistik Asymptotik Statistik Lehrbuch |
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| volume_link | (DE-604)BV000005407 |
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