Gelfand Contributions to the Theory and Application of Statistics

A Volume in Honor of Herbert Solomon
1. Auflage 2014
ISBN: 978-1-4832-6127-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 572 Seiten, Web PDF

Contributions to the Theory and Application of Statistics: A Volume in Honor of Herbert Solomon is a collection of 20 papers that cover the significant contributions of Herbert Solomon in the field of statistics. This text is organized into four sections encompassing 20 chapters. Each section defines an area in which Herb has made a contribution and the papers are ordered alphabetically. The first section consists of four papers in the area of operations research and applied probability, while the second section gathers six papers looking into problems in distribution theory and geometric probability. The third section contains five applied articles in the areas of law and justice, medicine, and psychology. The fourth section covers five papers that explore several inference issues. This book will be of value to statisticians and advance students.

Autoren/Hrsg.

Gelfand, Alan E.

Inhaltsverzeichnis

1;Front Cover;1
2;Contributions to the Theory and Application of Statistics: A Volume in Honor of Herbert Solomon;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;Preface;10
7;A Biographical Sketch of Herbert Solomon;12
8;Publications of Herbert Solomon;16
9;The Invited Contributors;22
10;List of Contributors;28
11;Part I: Operations Research and Applied Probability;30
11.1;CHAPTER 1. INEQUALITIES FOR DISTRIBUTIONS WITH INCREASING FAILURE RATE;32
11.1.1;I. INTRODUCTION;32
11.1.2;II. RENEWAL FUNCTION INEQUALITIES;36
11.1.3;III. EXPONENTIAL APPROXIMATIONS;42
11.1.4;IV. COMMENTS AND ADDITIONS;44
11.1.5;REFERENCES;44
11.2;CHAPTER 2. A MARKOV DECISION APPROACH TO NUCLEAR MATERIALS SAFEGUARDS;48
11.2.1;I. INTRODUCTION AND SUMMARY;48
11.2.2;II. SOME HISTORY: SHEWHART CHARTS, PAGE CUSUM AND SEQUENTIAL ANALYSIS;50
11.2.3;III. MORE HISTORY: KALMAN FILTERS, SMOOTHING, PREDICTION, AND TRACKING;55
11.2.4;IV. THE CHANGE POINT PROBLEMS;58
11.2.5;V. MARKOV DECISION MODEL;59
11.2.6;V. SUMMARY;68
11.2.7;REFERENCES;69
11.3;CHAPTER 3.
ON THE PERSISTENT RELEASE OF PARTICLES IN A FLUID FLOW;72
11.3.1;I. INTRODUCTION;72
11.3.2;II. PRELIMINARIES;74
11.3.3;III. DETERMINISTIC RELEASE OF PARTICLES;78
11.3.4;IV. RANDOM RELEASE OF PARTICLES;89
11.3.5;V. FURTHER PROBLEMS—EXTREMA;100
11.3.6;VI. CONCLUDING REMARKS;102
11.3.7;REFERENCES;103
11.4;CHAPTER 4. STATISTICAL INFERENCE FOR RANDOM PARAMETER MARKOV POPULATION PROCESS MODELS;104
11.4.1;I. INTRODUCTION;104
11.4.2;II. MARKOV POPULATION PROCESSES;108
11.4.3;III. EXAMPLES OF SIMPLE MARKOV POPULATION PROCESSES;109
11.4.4;IV. STATISTICAL INFERENCE FOR MARKOV POPULATION PROCESSES;113
11.4.5;V. EMPIRICAL BAYES METHODS;123
11.4.6;VI. SUMMARY AND FURTHER REMARKS;126
11.4.7;REFERENCES;127
12;Part II: Distribution Theory and Geometric Probability;130
12.1;CHAPTER 5. PROBABILISTIC-GEOMETRIC THEOREMS ARISING FROM THE ANALYSIS OF CONTINGENCY TABLES;132
12.1.1;I. INTRODUCTION;132
12.1.2;II. COVERING AND CONVOLUTIONS—A GEOMETRIC CONNECTION;134
12.1.3;III. GENERALIZED VARIANCE;145
12.1.4;REFERENCES;151
12.2;CHAPTER 6. SOME REMARKS ON EXCHANGEABLE NORMAL VARIABLES WITH APPLICATIONS;156
12.2.1;I. INTRODUCTION;156
12.2.2;II. SOME CONSEQUENCES AND OTHER CHARACTERISTICS OF THE DISTRIBUTION;161
12.2.3;III. A MORE GENERAL PROBLEM;163
12.2.4;IV. AN EXAMPLE;170
12.2.5;V. MULTIPLE COMPONENTS;172
12.2.6;VI. EXTENSIONS TO A FINITE INTERVAL;176
12.2.7;VII. EXTENSION TO SAMPLING FROM EXCHANGEABLE NORMAL VARIABLES;179
12.2.8;VIII. ACKNOWLEDGMENT;180
12.2.9;REFERENCES;180
12.3;CHAPTER 7. ASYMPTOTICS FOR THE RATIO OF MULTIPLE t-DENSITIES;184
12.3.1;I. INTRODUCTION;184
12.3.2;II. PRELIMINARIES;189
12.3.3;III. ASYMPTOTIC DENSITY RESULTS;194
12.3.4;IV. COMPUTING FRACTILES;201
12.3.5;ACKNOWLEDGMENT;205
12.3.6;REFERENCES;205
12.4;CHAPTER 8. PERIODOGRAM TESTING BASED ON SPACINGS;208
12.4.1;I. INTRODUCTION;208
12.4.2;II. THE ASYMPTOTIC EXPANSION;209
12.4.3;III. THE MODEL AND COMPUTATIONAL STRATEGY;213
12.4.4;IV. CRITICAL VALUES;216
12.4.5;REFERENCES;224
12.5;CHAPTER 9. TESTS FOR UNIFORMITY ARISING FROM A SERIES OF EVENTS;226
12.5.1;I. INTRODUCTION;226
12.5.2;II. ALTERNATIVES TO UNIFORMITY;228
12.5.3;III. TEST STATISTICS AND THE VARIOUS ALTERNATIVES;234
12.5.4;IV. FINAL REMARKS;243
12.5.5;REFERENCES;245
12.6;CHAPTER 10. SPATIAL CLASSIFICATION ERROR RATES RELATED TO PIXEL SIZE;250
12.7;I. INTRODUCTION;250
12.8;II. METHODS;252
12.9;III. CALCULATIONS;256
12.10;APPENDIX;260
12.11;REFERENCES;261
12.12;Part III: Applications;270
12.13;CHAPTER 11. THE USE OF PEREMPTORY CHALLENGES IN JURY SELECTION;272
12.13.1;I. INTRODUCTION AND SUMMARY;272
12.13.2;II. METHODS OF JURY SELECTION;273
12.13.3;III. NUMBERS OF PEREMPTORY CHALLENGES;277
12.13.4;IV. THE HISTORY OF JURIES AND SUPREME COURT DECISIONS;282
12.13.5;V. A MODEL OF THE JURY-SELCTION PROCESS;287
12.13.6;VI. OPTIMAL STRATEGIES;292
12.13.7;VII. CANADA;296
12.13.8;REFERENCES;298
12.14;CHAPTER 12.
AN INFORMATION-PROCESSING MODEL BASED ON REACTION TIMES IN SOLVING LINEAR EQUATIONS;302
12.14.1;I. THE PSYCHOLOGICAL MODEL;305
12.14.2;II. EXPERIMENTAL METHOD;314
12.14.3;III. STATISTICAL MODEL;317
12.14.4;IV. RESULTS OF A PILOT STUDY;323
12.14.5;V. SUMMARY;327
12.14.6;ACKNOWLEDGMENTS;328
12.14.7;REFERENCES;329
12.15;CHAPTER 13.
DIAGNOSTIC ERRORS AND THEIR IMPACT ON DISEASE TRENDS;332
12.15.1;I. INTRODUCTION;332
12.15.2;II. DIAGNOSTIC AND CERTIFICATION ERRORS;334
12.15.3;III. AUTOPSY CONFIRMATION;335
12.15.4;IV. CODIFICATION ERRORS;336
12.15.5;V. IMPLICATIONS TO TREND ANALYSIS;338
12.15.6;VI. DISCUSSION;341
12.15.7;CHRONOLOGICAL BIBLIOGRAPHY;345
12.16;CHAPTER 14.
HYPOTHESIS TESTING IN THE COURTROOM;360
12.16.1;I. INTRODUCTION;360
12.16.2;II. INFERENCE AND DECISION;363
12.16.3;III. THE BURDEN OF PERSUASION;367
12.16.4;IV. THE "EQUALIZED" TEST;370
12.16.5;V. A BAYESIAN TEST;374
12.16.6;VI. SOME ALTERNATIVES;378
12.16.7;VII. CONCLUSION;381
12.16.8;REFERENCES;383
12.17;CHAPTER 15.
MULTIVARIATE DISCRIMINATION OF DEPRESSIVE GROUPS ACROSS CULTURES;386
12.17.1;I. INTRODUCTION;386
12.17.2;II. METHOD;389
12.17.3;III. RESULTS;394
12.17.4;IV. COMMENT;399
12.17.5;ACKNOWLEDGMENTS;402
12.17.6;REFERENCES;403
12.18;Part IV: Inference Methodology;406
12.19;CHAPTER 16.
ESTIMATION IN PARAMETRIC MIXTURE FAMILIES;408
12.19.1;I. INTRODUCTION;408
12.19.2;II. IMPROVING UPON UNBIASED ESTIMATORS;409
12.19.3;III. BAYES ESTIMATION;413
12.19.4;IV. PARAMETRIC EMPIRICAL BAYES ESTIMATION;417
12.19.5;ACKNOWLEDGMENT;424
12.19.6;REFERENCES;424
12.20;CHAPTER 17.
MULTIPLE SHRINKAGE GENERALIZATIONS OF THE JAMES-STEIN ESTIMATOR;426
12.20.1;I. INTRODUCTION;426
12.20.2;II. A CLASS OF MULTIPLE SHRINKAGE GENERALIZATIONS;431
12.20.3;III. RISK CONSIDERATIONS;438
12.20.4;IV. MOTIVATIONS;448
12.20.5;V. ACKNOWLEDGMENT;455
12.20.6;REFERENCES;455
12.21;CHAPTER 18.
THE ANALYSIS OF A SET OF MULTIDIMENSIONAL CONTINGENCY TABLES USING LOG-LINEAR MODELS, LATENT-CLASS MODELS, AND CORRELATION MODELS: THE SOLOMON DATA REVISITED;458
12.21.1;I. INTRODUCTION;458
12.21.2;II. THE SOLOMON DATA;460
12.21.3;III. SOME LOG-LINEAR MODELS;462
12.21.4;IV. SOME LATENT-CLASS MODELS;484
12.21.5;V. SOME MULTIVARIATE CORRELATION MODELS;501
12.21.6;ACKNOWLEDGMENTS;509
12.21.7;REFERENCES;509
12.22;CHAPTER 19.
SELECTION PROCEDURE FOR MULTINOMIAL POPULATIONS WITH RESPECT TO DIVERSITY INDICES;514
12.22.1;I. INTRODUCTION;514
12.22.2;II. DIVERSITY-MEASURE AND THEIR ESTIMATES;521
12.22.3;III. PROCEDURES FOR SELECTING THE MOST DIVERSE POPULATION;527
12.22.4;IV. PROCEDURES FOR SELECTING A SUBSET CONTAINING THE MOST DIVERSE POPULATION;532
12.22.5;REFERENCES;537
12.23;CHAPTER 20.
CONFIDENCE INTERVALS FOR THE COMMON VARIANCE OF EQUICORRELATED NORMAL RANDOM VARIABLES;540
12.23.1;I. INTRODUCTION;540
12.23.2;II. THE MODEL, THE LIKELIHOOD FUNCTION AND FISHER INFORMATION;543
12.23.3;III. POINT AND INTERVAL ESTIMATORS BASED ON THE MLE;547
12.23.4;IV. DETERMINATION OF THE EXACT COVERAGE PROBABILITY AND EXPECTED LENGTH OF THE MLE-BASED INTERVALS;549
12.23.5;V. ESTIMATED - p INTERVALS;554
12.23.6;VI. THE LOSS OF COVERAGE IN ASSUMING p = o;563
12.23.7;VII. THE RELATIVE EFFICIENCY OF INTERVAL ESTIMATORS;564
12.23.8;VIII. DISCUSSION AND CONCLUSION;568
12.23.9;REFERENCES;573