Gupta / Moore Statistical Decision Theory and Related Topics

Proceedings of a Symposium Held at Purdue University, May 17-19, 1976
1. Auflage 2014
ISBN: 978-1-4832-6031-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 492 Seiten, Web PDF

Statistical Decision Theory and Related Topics II is a compendium of papers presented at an international symposium on Statistical Decision Theory and Related Topics held at Purdue University in May, 1976. The researchers invited to participate, and to author papers for this volume, are among the leaders in the field of Statistical Decision Theory. This collection features works on general decision theory, multiple decision theory, optimal experimental design, and robustness. Mathematicians and statisticians will find the book highly insightful and informative.

Autoren/Hrsg.

Gupta, Shanti S.

Moore, David S.

Inhaltsverzeichnis

1;Front Cover;1
2;Statistical Decision Theory and Related Topics II;4
3;Copyright Page;5
4;Table of Contents;6
5;CONTRIBUTORS TO THE SYMPOSIUM;10
6;PREFACE;14
7;CHAPTER 1. SELECTING THE LARGEST INTERACTION IN A TWO-FACTOR EXPERIMENT;16
7.1;1. Introduction;16
7.2;2. Model and Statistical as sumptions;17
7.3;4. Selection procedure, and the choice of sample size;19
7.4;5. Expression for the PCS;20
7.5;6. LF-configuration of the yij for the 2xc case;21
7.6;7. Directions of future research;30
7.7;8. Acknowledgment;31
7.8;References;32
8;CHAPTER 2. IMPROVED MINIMAX ESTIMATORS OF NORMAL MEAN VECTORS FOR CERTAIN TYPES OF COVARIANCE MATRICES;34
8.1;1. Introduction;34
8.2;2. Basic results;36
8.3;3. Applications;45
8.4;References;50
9;CHAPTER 3. ON SELECTING A SET OF GOOD POPULATIONS;52
9.1;1. Introduction;52
9.2;2. Notation and statement of the problem;53
9.3;3. The optimal invariant procedure;55
9.4;4. The number of populations is large;57
9.5;5. Unknown µ*: Bayes, empirical Bayes and compound theory;63
9.6;Appendix;65
9.7;References;70
10;CHAPTER 4. CLOSURE THEOREMS FOR SEQUENTIAL-DESIGN PROCESSES;72
10.1;1. Introduction;72
10.2;2. Description of the process;76
10.3;3. Basic theorems for a compact action space;85
10.4;4. Basic theorems for general actions spaces;93
10.5;5. Bayes procedures;98
10.6;6. Available actions dependent on past observations;100
10.7;7.
Dynamic programming;101
10.8;References;105
11;CHAPTER 5. A SUBSET SELECTION PROBLEM EMPLOYING A NEW CRITERION;108
11.1;1. Introduction and summary;108
11.2;2. Loss function;108
11.3;3. Normal model;109
11.4;4. Computations;111
11.5;5. Comparison of stategies;112
11.6;6. Estimates based on Monte Carlo Calculations;116
11.7;7. Polemics;117
11.8;APPENDIX;122
11.9;References;126
12;CHAPTER 6. EXAMPLES RELEVANT TO THE ROBUSTNESS OF APPLIED INFERENCES;136
12.1;1. Introdcution;136
12.2;2. Bayesian robustness;138
12.3;3. Examples;141
12.4;4. Concluding remark;152
12.5;References;153
13;CHAPTER 7. ON SOME r-MINIMAX SELECTION AND MULTIPLE COMPARISON PROCEDURES;154
13.1;1. Introduction;154
13.2;2. Selection procedures for the "best" populations;155
13.3;References;168
14;CHAPTER 8. MORE ON INCOMPLETE AND BOUNDEDLY COMPLETE FAMILIES OF DISTRIBUTIONS;172
14.1;1. Introduction;172
14.2;2. Distributions symmetric about;174
14.3;3. Two-sample families;174
14.4;4. Families restricted by a nonlinear condition;176
14.5;References;179
15;CHAPTER 9. ROBUST COVARIANCES;180
15.1;1. Introduction;180
15.2;2. Maximum likelihood estimates;181
15.3;3. Estimates determined by implicit equations;183
15.4;4. Breakdown properties;185
15.5;5. A note on computation;187
15.6;6. Large samples properties;190
15.7;7. Least informative distributions: location;193
15.8;8. Least informative distributions: covariance;195
15.9;9. Spherical symmetry? A note on models;199
15.10;Appendix;201
15.11;Acknowledgement;205
15.12;References;206
16;CHAPTER 10. ASYMPTOTICALLY MINIMAX ESTIMATION OF CONCAVE AND CONVEX DISTRIBUTION FUNCTIONS. II;208
16.1;0. Introduction;208
16.2;5. Estimating concave F under conditions (5.3);209
17;CHAPTER 11. SEQUENTIAL DECISION ABOUT A NORMAL MEAN;228
17.1;1. Introduction;228
17.2;2. Probability of error;230
17.3;3. Expected sample size;232
17.4;References;235
18;CHAPTER 12.
A REDUCTION THEOREM FOR CERTAIN SEQUENTIAL EXPERIMENTS;238
18.1;1. Introduction;238
18.2;2. Notation and main assumptions;239
18.3;3. A reduction procedure;246
18.4;4. Independent observations;250
18.5;5. Some applications to tests and estimates;254
18.6;References;259
19;CHAPTER 13. ROBUST DESIGNS FOR REGRESSION PROBLEMS;260
19.1;1. Introduction;260
19.2;2. Formulation of the problem;262
19.3;3. Solutions;270
19.4;4. Standard estimates;278
19.5;References;283
20;CHAPTER 14. LARGE SAMPLE PROPERTIES OF NEAREST NEIGHBOR DENSITY FUNCTION ESTIMATORS;284
20.1;1. Introduction;284
20.2;2. Almost sure consistency, uniform kernel case;286
20.3;3. Asymptotic normality, uniform kernel case;288
20.4;4. Asymptotic normality, general case;289
20.5;References;294
21;CHAPTER 15. A STOCHASTIC VERSION OF WEAK MAJORIZATION, WITH APPLICATIONS;296
21.1;1. Introduction;296
21.2;2. A stochastic version of weak majorization;296
21.3;3. Preservation of stochastic weak majorization under;301
21.4;References;310
22;CHAPTER 16. SYNERGISTIC EFFECTS AND THE CORRESPONDING OPTIMAL VERSION OF THE MULTIPLE COMPARISON PROBLEM;312
22.1;1. Introduction;312
22.2;2. Early times;313
22.3;3. Bartlett's priority in treating a questionnaire relating;319
22.4;4. Enter Hotelling and confidence regions;319
22.5;5. Development after World War II;321
22.6;6. What is the outstanding theoretical-statistical problem;322
22.7;7. Concluding remarks;325
22.8;References;325
23;CHAPTER 17.
ESTIMATING COVARIANCES IN A MULTIVARIATE NORMAL DISTRIBUTION;328
23.1;1. Introduction;328
23.2;2. Preliminaries;329
23.3;3. Estimation of covariances;331
23.4;4. Estimation of the variance when the mean is unknown in a univariate normal distribution;338
23.5;References;340
24;CHAPTER 18. SIMULTANEOUS ESTIMATION OF PARAMETERS -A COMPOUND DECISION PROBLEM;342
24.1;1. Introduction;342
24.2;2. The problem of simultaneous estimation;344
24.3;3. Direct and inverse regression estimates;345
24.4;4. Estimation of parameters with an underlying stochastic;354
24.5;5. Gauss-Markoff model;356
24.6;6. Simultaneous estimation of vector parameters -the problem of selection index;357
24.7;References;363
25;CHAPTER 19. ROBUST BAYESIAN ESTIMATION;366
25.1;1. Motivation;366
25.2;2. The specific problem and procedures;367
25.3;3. Results;368
25.4;4. Conclusions;369
25.5;References;370
26;CHAPTER 20.
THE DIRICHLET-TYPE 1 INTEGRAL AND ITS APPLICATIONS TO MULTINOMIAL-RELATED PROBLEMS;372
26.1;1. Introduction;372
26.2;2. Basic recurrence relation;373
26.3;3. Derivatives and differences;375
26.4;4. Dual quantities and generalizations;377
26.5;5. Combinatorial aspects and generalized Stirling numbers;379
26.6;6. Some applications of Dirichlet-type 1;382
26.7;References;389
27;CHAPTER 21. OPTIMAL SEARCH DESIGNS, OR DESIGNS OPTIMAL UNDER BIAS FREE OPTIMALITY CRITERIA;390
27.1;1. Introduction;390
27.2;2. Search linear models;393
27.3;3. Factorial designs;397
27.4;4. Optimum search designs;400
27.5;5. DD-optimality;409
27.6;6. "Main effect plus plans for 2m factorials;412
27.7;7. "Bypassing" search: Block designs with multi-dimensional blocks;419
27.8;8. Some numerical results on resolution 5.1 designs;421
27.9;References;422
28;CHAPTER 22.
OPTIMAL DESIGNS FOR INTEGRATED VARIANCE IN POLYNOMIAL REGRESSION;426
28.1;1. Introduction;426
28.2;2. General procedure;427
28.3;3. Bounds on error and s = constant;431
28.4;References;435
29;CHAPTER 23. ASYMPTOTIC EXPANSIONS FOR THE DISTRIBUTION FUNCTIONS OF LINEAR COMBINATIONS OF ORDER STATISTICS;436
29.1;1. Introduction;436
29.2;2. Edgeworth expansions;437
29.3;3. Linear combinations of order statistics;441
29.4;4. A bound on the characteristic function;446
29.5;References;451
30;CHAPTER 24. ASYMPTOTIC PROPERTIES OF BAYES TESTS OF NONPARAMETRIC HYPOTHESES;454
30.1;1. Introduction;454
30.2;2. Some tests of fit;457
30.3;References;465
31;CHAPTER 25. OBSTRUCTIVE DISTRIBUTIONS IN A SEQUENTIAL RANK-ORDER TEST BASED ON LEHMANN ALTERNATIVES;466
31.1;1. Introduction;466
31.2;2. The main results;468
31.3;3. Proof of Propositions 2.1;471
31.4;4. Proof of Proposition;474
31.5;5. Proof of Proposition 2.4;477
31.6;6. An example of an obstructive discrete P;479
31.7;References;484
32;CHAPTER 26. OPTIMUM DESIGNS FOR FINITE POPULATIONS SAMPLING;486
32.1;1. Statistical motivation;486
32.2;2. Continuous generalization;487
32.3;3. Examples;492
32.4;References;493