Mathematical statistics: a decision theoretic approach
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York [u.a.]
Acad. Press
1973
|
| Ausgabe: | 4. print. |
| Schriftenreihe: | Probability and mathematical statistics
1 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000570145&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XI, 396 S. |
Internformat
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| 245 | 1 | 0 | |a Mathematical statistics |b a decision theoretic approach |c Thomas S. Ferguson |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface v
chapter 1. Game Theory and Decision Theory
1.1 Basic Elements 1
1.2 A Comparison of Game Theory and Decision
Theory 5
1.3 Decision Function; Risk Function 6
1.4 Utility and Subjective Probability 11
1.5 Randomization 22
1.6 Optimal Decision Rules 28
1.7 Geometric Interpretation for Finite 0 34
1.8 The Form of Bayes Rules for Estimation
Problems 43
chapter 2. The Main Theorems of Decision Theory
2.1 Admissibility and Completeness 54
2.2 Decision Theory 56
2.3 Admissibility of Bayes Rules 59
2.4 Basic Assumptions 63
2.5 Existence of Bayes Decision Rules 67
ix
x • Contents
2.6 Existence of a Minimal Complete Class 69
2.7 The Separating Hyperplane Theorem 70
2.8 Essential Completeness of the Class of
Nonrandomized Decision Rules 76
2.9 The Minimax Theorem 81
2.10 The Complete Class Theorem 86
2.11 Solving for Minimax Rules 90
chapter 3. Distributions and Sufficient Statistics
3.1 Useful TJnivariate Distributions 98
3.2 The Multivariate Normal Distribution 105
3.3 Sufficient Statistics 112
3.4 Essentially Complete Classes of Rules Based on
Sufficient Statistics 119
3.5 Exponential Families of Distributions 125
3.6 Complete Sufficient Statistics 132
3.7 Continuity of the Risk Function 137
chapter 4. Invariant Statistical Decision Problems
4.1 Invariant Decision Problems 143
4.2 Invariant Decision Rules 148
4.3 Admissible and Minimax Invariant Rules 154
4.4 Location and Scale Parameters 164
4.5 Minimax Estimates of Location Parameters 166
4.6 Minimax Estimates for the Parameters of a
Normal Distribution 176
4.7 The Pitman Estimate 186
4.8 Estimation of a Distribution Function 191
chapter 5. Testing Hypotheses
5.1 The Neyman Pearson Lemma 198
5.2 Uniformly Most Powerful Tests 206
5.3 Two Sided Tests 215
5.4 Uniformly Most Powerful Unbiased Tests 224
5.5 Locally Best Tests 235
5.6 Invariance in Hypothesis Testing 242
5.7 The Two Sample Problem 250
5.8 Confidence Sets 257
5.9 The General Linear Hypothesis 264
5.10 Confidence Ellipsoids and Multiple Comparisons 274
Contents • xi
chapter 6. Multiple Decision Problems
6.1 Monotone Multiple Decision Problems 284
6.2 Bayes Rules in Multiple Decision Problems 291
6.3 Slippage Problems 299
chapter 7. Sequential Decision Problems
7.1 Sequential Decision Rules 309
7.2 Bayes and Minimax Sequential Decision Rules 313
7.3 Convex Loss and Sufficiency 329
7.4 Invariant Sequential Decision Problems 340
7.5 Sequential Tests of a Simple Hypothesis Against
a Simple Alternative 350
7.6 The Sequential Probability Ratio Test 361
7.7 The Fundamental Identity of Sequential Analysis 370
References 388
Subject Index 393
|
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| id | DE-604.BV000930638 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T07:28:48Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000570145 |
| oclc_num | 256286997 |
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| physical | XI, 396 S. |
| publishDate | 1973 |
| publishDateSearch | 1973 |
| publishDateSort | 1973 |
| publisher | Acad. Press |
| record_format | marc |
| series | Probability and mathematical statistics |
| series2 | Probability and mathematical statistics |
| spellingShingle | Ferguson, Thomas S. 1929- Mathematical statistics a decision theoretic approach Probability and mathematical statistics Entscheidungstheorie (DE-588)4138606-1 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4138606-1 (DE-588)4056995-0 |
| title | Mathematical statistics a decision theoretic approach |
| title_auth | Mathematical statistics a decision theoretic approach |
| title_exact_search | Mathematical statistics a decision theoretic approach |
| title_full | Mathematical statistics a decision theoretic approach Thomas S. Ferguson |
| title_fullStr | Mathematical statistics a decision theoretic approach Thomas S. Ferguson |
| title_full_unstemmed | Mathematical statistics a decision theoretic approach Thomas S. Ferguson |
| title_short | Mathematical statistics |
| title_sort | mathematical statistics a decision theoretic approach |
| title_sub | a decision theoretic approach |
| topic | Entscheidungstheorie (DE-588)4138606-1 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Entscheidungstheorie Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000570145&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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