Gupta / Berger Statistical Decision Theory and Related Topics III

1. Auflage 2014
ISBN: 978-1-4832-5955-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 550 Seiten, Web PDF

Statistical Decision Theory and Related Topics III, Volume 2 is a collection of papers presented at the Third Purdue Symposium on Statistical Decision Theory and Related Topics, held at Purdue University in June 1981. The symposium brought together many prominent leaders and a number of younger researchers in statistical decision theory and related areas. This volume contains the research papers presented at the symposium and includes works on general decision theory, multiple decision theory, optimum experimental design, sequential and adaptive inference, Bayesian analysis, robustness, and large sample theory. These research areas have seen rapid developments since the preceding Purdue Symposium in 1976, developments reflected by the variety and depth of the works in this volume. Statisticians and mathematicians will find the book very insightful.

Autoren/Hrsg.

Gupta, Shanti S.

Berger, James O.

Inhaltsverzeichnis

1;Front Cover;1
2;Statistical Decision Theory and Related Topics III;4
3;Copyright Page;5
4;Table of Contents;6
5;CONTRIBUTORS;10
6;PREFACE;14
7;CONTENTS OF VOLUME 1;16
8;CHAPTER 1. SOME LOCALLY OPTIMAL SUBSET SELECTION RULES BASED ON RANKS;18
8.1;I. INTRODUCTION;18
8.2;II. SELECTING THE BEST POPULATION;19
8.3;III. COMPARISON WITH A CONTROL;25
8.4;REFERENCES;30
9;CHAPTER 2. CERTAIN BOUNDS ON THE CLASS OF ADMISSIBLE ESTIMATORS IN CONTINUOUS EXPONENTIAL FAMILIES;32
9.1;I. INTRODUCTION;32
9.2;II. A PRELIMINARY LEMMA;34
9.3;III. INADMISSIBILITY RESULTS;36
9.4;IV. REMARKS AND GENERALIZATIONS;44
9.5;ACKNOWLEDGMENT;45
9.6;REFERENCES;45
10;CHAPTER 3. RIDGE TYPE ESTIMATORS OF MULTINOMIAL CELL PROBABILITIES;48
10.1;I. INTRODUCTION AND SUMMARY;48
10.2;II. RIDGE ESTIMATION;49
10.3;III. RIDGE ESTIMATORS OF p;53
10.4;IV. SMALL SAMPLE SITUATIONS;59
10.5;V. DISCUSSION;66
10.6;ACKNOWLEDGMENT;67
10.7;REFERENCES;67
11;CHAPTER 4. ASYMPTOTICALLY OPTIMAL PROCEDURES FOR SEQUENTIAL ADAPTIVE SELECTION OF THE BEST OF SEVERAL NORMAL MEANS;72
11.1;1. INTRODUCTION;72
11.2;II. ELIMINATION PROCEDURES WITH VECTOR AT A TIME SAMPLING;74
11.3;III. ELIMINATION PROCEDURES WITH ADAPTIVE SAMPLING;86
11.4;REFERENCES;102
12;CHAPTER 5. MODEL ROBUST CONFIDENCE INTERVALS II;104
12.1;I. INTRODUCTION;104
12.2;II. CONFIDENCE INTERVAL;106
12.3;III. CONFIDENCE BANDS;112
12.4;REFERENCES;118
13;CHAPTER 6. ADAPTIVE DESIGN AND THE MULTIPERIOD CONTROL PROBLEM;120
13.1;I. INTRODUCTION AND SUMMARY;120
13.2;II. BAYES SOLUTION TO THE MULTIPERIOD CONTROL PROBLEM IN THE CASE OF KNOWN ß;126
13.3;REFERENCES;137
14;CHAPTER 7. ON THE RISK OF BAYES ESTIMATES;138
14.1;I. INTRODUCTION;138
14.2;II. MAIN ASSUMPTIONS AND GENERAL INEQUALITIES;139
14.3;III. TESTS BETWEEN HELLINGER BALLS;142
14.4;IV. BOUNDS ON BAYES RISKS;145
14.5;V. COMPARISON WITH OTHER ESTIMATES;151
14.6;REFERENCES;153
15;CHAPTER 8. THE MINIMAL· COMPLETE CLASS OF PROCEDURES FOR COMBINING INDEPENDENT NONCENTRAL F-TESTS;156
15.1;I. INTRODUCTION;156
15.2;II. COMPLETE CLASS RESULTS;159
15.3;III. THE CONSTANT r(v, µ);162
15.4;IV. PRELIMINARIES FOR THE NONPARAMETRIC TESTS;166
15.5;V. INVERSE NORMAL PROCEDURE (1.10);169
15.6;VI. INVERSE LOGISTIC PROCEDURE (1.11);173
15.7;VII. SUMS OF pi 's (1.12);177
15.8;VIII. FISHER'S PARAMETRIC TEST (1. 3);189
15.9;IX. THE TEST (1.14);191
15.10;APPENDIX: COMPUTATIONS;192
15.11;REFERENCES;198
16;CHAPTER 9. RIDGE ESTIMATORS AS CONSTRAINED GENERALIZED LEAST SQUARES;200
16.1;I. INTRODUCTION;200
16.2;II. CONVEXITY OF THE GENERALIZED SUM OF SQUARES AND CONCAVITY OF THE CONSTRAINT;202
16.3;III. CONSTRAINED OPTIMIZATION;204
16.4;IV. CONCLUDING REMARKS;206
16.5;ACKNOWLEDGEMENT;207
16.6;REFERENCES;207
17;CHAPTER 10. BOUNDS FOR A K-FOLD INTEGRAL FOR LOCATION AND SCALE PARAMETER MODELS WITH APPLICATIONS TO STATISTICAL RANKING AND SELECTION PROBLEMS;210
17.1;I. INTRODUCTION;210
17.2;II. THE MAIN BOUNDS;212
17.3;III. APPROXIMATIONS;215
17.4;IV. LIMITING DISTRIBUTION OF THE ESTIMATOR OF THE PCS FOR THE LOCATION PARAMETER MODEL;217
17.5;V. BOUNDS ON THE PROBABILITY FUNCTION OF A CORRECT COMPLETE RANKING;222
17.6;APPENDIX TO SECTION 3;226
17.7;REFERENCES;227
18;CHAPTER 11. THE ASYMPTOTIC DISTRIBUTION THEORY OF ONE SAMPLE SIGNED RANK STATISTIC;230
18.1;I. INTRODUCTION;230
18.2;II. PRELIMINARIES;231
18.3;III. THE ASYMPTOTIC NORMALITY OF SN+;233
18.4;IV. THE RATE OF CONVERGENCE;243
18.5;ACKNOWLEDGMENT;247
18.6;REFERENCES;247
19;CHAPTER 12. ANALYSIS OF DIVERSITY: A UNIFIED APPROACH;250
19.1;I. INTRODUCTION;250
19.2;II. MEASURES OF DIVERSITY AND ITS USES;251
19.3;III. CONSTRUCTION OF DIVERSITY MEASURES;254
19.4;IV. SAMPLING THEORY;259
19.5;V. ENTROPY AS A DIVERSITY MEASURE;264
19.6;REFERENCES;266
20;CHAPTER 13. ESTIMATING MANY VARIANCES;268
20.1;REFERENCES;278
21;CHAPTER 14. ESTIMATING A POSSIBLY RATIONAL MEAN;280
21.1;I. PRELIMINARIES;280
21.2;II. CASE OF A POSSIBLY FIXED MEAN;281
21.3;III. CASE OF A POSSIBLY INTEGER MEAN;282
21.4;IV. CASE OF A POSSIBLY RATIONAL MEAN;283
21.5;V. SUMMARY;285
21.6;REFERENCE;285
22;CHAPTER 15. ADAPTIVE PROCEDURES FOR A FINITE NUMBER OF PROBABILITY DISTRIBUTION FAMILIES;286
22.1;I. INTRODUCTION;286
22.2;II. THE ASYMPTOTICAL BEHAVIOR OF MINIMAX ESTIMATORS;288
22.3;III. THE EXISTENCE OF ADAPTIVE PROCEDURES;294
22.4;REFERENCES;301
23;CHAPTER 16. IMPROVEMENTS ON LINEAR MINIMAX ESTIMATES;304
23.1;I. INTRODUCTION;304
23.2;II. REGRESSION WITH f LIPSCHITZ;308
23.3;III. DENSITY ESTIMATION;311
23.4;IV. EXTENSIONS AND REMARKS;316
23.5;REFERENCES;321
24;CHAPTER 17. CONVERGENCE OF DIRICHLET MEASURES AND THE INTERPRETATION OF THEIR PARAMETER;322
24.1;I. INTRODUCTION;322
24.2;II. THE DIRICHLET MEASURE;323
24.3;III. CONVERGENCE OF DIRICHLET MEASURES;325
24.4;IV. CONVERGENCE OF BAYES ESTIMATES;329
24.5;ACKNOWLEDGMENTS;331
24.6;REFERENCES;332
25;CHAPTER 18. ADMISSIBILITY AND LOCAL ASYMPTOTIC ADMISSIBILITY OF PROCEDURES WHICH COMBINE ESTIMATION AND MODEL SELECTION;334
25.1;I. STATEMENT OF RESULTS;334
25.2;II. PROOF OF THEOREM 1;339
25.3;III. PROOF OF THEOREM 2;346
25.4;REFERENCES;349
26;CHAPTER 19. OPTIMAL DESIGNS FOR WEIGHTED POLYNOMIAL REGRESSION USING CANONICAL MOMENTS;352
26.1;I. INTRODUCTION;352
26.2;II. CANONICAL MOMENTS AND TECHNICAL LEMMAS;355
26.3;III. D-OPTIMALITY FOR CLASSICAL WEIGHTS;362
26.4;IV. D -OPTIMAL DESIGNS FOR w(x) = x, 1-x OR x(1-x);364
26.5;REFERENCES;366
27;CHAPTER 20. HIGHER ORDER ASYMPTOTIC EFFICIENCY OF ESTIMATORS IN DECISION PROCEDURES;368
27.1;I. INTRODUCTION;368
27.2;II. CONSISTENCY;369
27.3;III. ASYMPTOTIC EFFICIENCY;372
27.4;REFERENCES;378
28;CHAPTER 21. DECISION-THEORETIC REGRESSION DIAGNOSTICS;380
28.1;I. INTRODUCTION;380
28.2;II. REGRESSION AND DIAGNOSTICS;381
28.3;III. STRUCTURE OF STATISTICAL PROBLEMS;383
28.4;IV. TWO REGRESSION MODELS;384
28.5;V. MINIMIAX RESULTS;387
28.6;VI. MULTICOLLINEARITY DIAGNOSTICS;389
28.7;VII. AN OLD DIAGNOSTIC;393
28.8;VII. ON LOSS FUNCTIONS;395
28.9;REFERENCES;397
29;CHAPTER 22. CONSTRAINED REGULARIZATION FOR ILL POSED LINEAR OPERATOR EQUATIONS, WITH APPLICATIONS IN METEOROLOGY AND MEDICINE;400
29.1;I. INTRODUCTION;400
29.2;II. SOME APPLICATIONS;405
29.3;III. CROSS VALIDATION FOR CONSTRAINED PROBLEMS;407
29.4;IV. NUMERICAL EXPERIMENTS;413
29.5;ACKNOWLEDGMENTS;430
29.6;REFERENCES;430
30;CHAPTER 23. DATA FUSION;436
30.1;I. INTRODUCTION;436
30.2;II. DATA FUSION;437
30.3;III. AXIOMATICS;438
30.4;IV. FUSION SPACE STRUCTURE;439
30.5;V. SOME EXAMPLES;443
30.6;VI. PARTIAL ORDERS;448
30.7;REFERENCES;449
31;CHAPTER 24. SEQUENTIAL CONFIDENCE SETS: ESTIMATION-ORIENTED VERSUS TEST-ORIENTED CONSTRUCTION;452
31.1;I. INTRODUCTION;452
31.2;II. ESTIMATION-ORIENTED CONFIDENCE INTERVALS;455
31.3;III. COMPARISON BETWEEN ESTIMATION-ORIENTED AND TEST-ORIENTED CI's;461
31.4;IV. DISCUSSION AND CONCLUSIONS;465
31.5;ACKNOWLEDGEMENT;467
31.6;REFERENCES;467
32;CHAPTER 25. INCORPORATING PRIOR INFORMATION IN MINIMAX ESTIMATION OF THE MEAN OF A GAUSSIAN PROCESS;468
32.1;I. INTRODUCTION;468
32.2;II. THE MINIMAX ESTIMATOR;470
32.3;III. ANALYSIS WHEN G AND . COMMUTE;477
32.4;REFERENCES;481
33;CHAPTER 26. EMPIRICAL BAYES ESTIMATION OF THE MEAN OF A NORMAL DISTRIBUTION WITH CONVEX LOSS;482
33.1;I. INTRODUCTION;482
33.2;II. THE EMPIRICAL BAYESIAN MODEL;483
33.3;III. ASYMPTOTICS;488
33.4;IV. HOMOGENEOUS LOSS;497
33.5;REFERENCES;501
34;CHAPTER 27. OPTIMUM SUBMEASURES WITH APPLICATION TO FINITE POPULATION SAMPLING;502
34.1;I. INTRODUCTION;502
34.2;II. SUB-MEASURES;503
34.3;III. OPTIMUM SUB-MEASURES;505
34.4;IV. REGRESSION EXPERIMENTS;508
34.5;V. COMPUTATION AND DISCRETIZATION;510
34.6;REFERENCES;512
35;CHAPTER 28. ON MATCHMAKING;514
35.1;I. INTRODUCTION;514
35.2;II. COMPUTATION;515
35.3;III. EXAMPLE;517
35.4;IV. REMARKS;520
35.5;REFERENCES;520
36;CHAPTER 29. A CLASS OF GENERALIZED BAYES MINIMAX ESTIMATORS;522
36.1;I. INTRODUCTION;522
36.2;II. MINIMAXITY;523
36.3;III. ADMISSIBILITY AND INADMISSIBILITY;535
36.4;IV. SELECTING AN ESTIMATOR;537
36.5;ACKNOWLEDGMENTS;551
36.6;REFERENCES;551