Shanti S. Gupta has made pioneering contributions to ranking and selection theory; in particular, to subset selection theory. His list of publications and the numerous citations his publications have received over the last forty years will amply testify to this fact. Besides ranking and selection, his interests include order statistics and reliability theory. The first editor's association with Shanti Gupta goes back to 1965 when he came to Purdue to do his Ph.D. He has the good fortune of being a student, a colleague and a long-standing collaborator of Shanti Gupta. The second editor's association with Shanti Gupta began in 1978 when he started his research in the area of order statistics. During the past twenty years, he has collaborated with Shanti Gupta on several publications. We both feel that our lives have been enriched by our association with him. He has indeed been a friend, philosopher and guide to us.
I: Bayesian Inference.- 1 Bayes for Beginners? Some Pedagogical Questions.- 1.1 Introduction.- 1.2 Unfinished Business: The Position of Bayesian Methods.- 1.3 The Standard Choice.- 1.4 Is Bayesian Reasoning Accessible?.- 1.5 Probability and Its Discontents.- 1.6 Barriers to Bayesian Understanding.- 1.7 Are Bayesian Conclusions Clear?.- 1.8 What Spirit for Elementary Statistics Instruction?.- References.- 2 Normal Means Revisited.- 2.1 Introduction.- 2.2 Selection Criteria.- 2.3 Model and Computations.- 2.4 Numerical Example.- References.- 3 Bayes m-Truncated Sampling Allocations for Selecting the Best Bernoulli Population.- 3.1 Introduction.- 3.2 General Outline of Bayes Sequential Sampling Allocations.- 3.3 Allocations for Bernoulli Populations.- 3.4 Numerical Results and Comparisons.- References.- 4 On Hierarchical Bayesian Estimation and Selection for Multivariate Hypergeometric Distributions.- 4.1 Introduction.- 4.2 Formulation of the Problems.- 4.2.1 Bayesian estimation of si, i=1,..., n.- 4.2.2 Bayesian selection rule.- 4.3 A Hierarchical Bayesian Approach.- 4.4 Optimality of the Hierarchical Bayesian Procedures.- 4.4.1 Optimality of ?H.- 4.4.2 Optimality of ?H.- References.- 5 Convergence Rates of Empirical Bayes Estimation and Selection for Exponential Populations With Location Parameters.- 5.1 Introduction.- 5.2 Bayes Estimators and Bayes Selection Rule.- 5.3 Empirical Bayes Estimators and Empirical Bayes Selection Rule.- 5.4 Asymptotic Optimality of the Empirical Bayes Estimators.- 5.5 Asymptotic Optimality of the Empirical Bayes Selection Rule.- 5.6 An Example.- References.- 6 Empirical Bayes Rules for Selecting the Best Uniform Populations.- 6.1 Introduction.- 6.2 Empirical Bayes Framework of the Selection Problem.- 6.3 Estimation of the Prior Distribution.- 6.3.1 Construction of the prior estimator.- 6.3.2 Consistency of the estimator.- 6.4 The Proposed Empirical Bayes Selection Procedure.- 6.5 Rates of Convergence.- References.- II: Decision Theory.- 7 Adaptive Multiple Decision Procedures for Exponential Families.- 7.1 Introduction.- 7.2 Adaptation for Exponential Families.- 7.3 Gamma Distributions Family.- 7.4 Normal Family.- References.- 8 Non-Informative Priors Via Sieves and Packing Numbers.- 8.1 Introduction.- 8.2 Preliminaries.- 8.3 Jeffreys' Prior.- 8.4 An Infinite Dimensional Example.- References.- III: Point And Interval Estimation-Classical Approach.- 9 From Neyman's Frequentism to the Frequency Validity in the Conditional Inference.- 9.1 Introduction.- 9.2 Frequency Validity under Model 1.- 9.3 Generalizations.- 9.3.1 Other statistical procedures.- 9.3.2 Frequency validity under Model 2 involving different experiments.- 9.4 Conclusions.- References.- 10 Asymptotic Theory for the Simex Estimator in Measurement Error Models.- 10.1 Introduction.- 10.2 The SIMEX Method.- 10.2.1 Simulation step.- 10.2.2 Extrapolation step.- 10.2.3 Sketch of asymptotics when B = ?.- 10.3 General Result and Logistic Regression.- 10.3.1 The general result.- 10.3.2 Logistic regression.- 10.4 SIMEX Estimation in Simple Linear Regression.- References.- 11 A Change Point Problem for Some Conditional Functionals.- 11.1 Introduction.- 11.2 Regularity Conditions and the Main Result.- 11.3 Some Discussions.- References.- 12 On Bias Reduction Methods in Nonparametric Regression Estimation.- 12.1 Introduction.- 12.2 The Bias Reduction Methods.- 12.3 A Monte Carlo Study.- References.- 13 Multiple Comparisons With the Mean.- 13.1 Different Types of Multiple Comparisons.- 13.2 Balanced MCM.- 13.3 Unbalanced MCM.- 13.3.1 Comparisons with the weighted mean.- 13.3.2 Comparisons with the unweighted mean.- 13.4 Recommendations.- References.- IV: Tests Of Hypotheses.- 14 Properties of Unified Bayesian-Frequentist Tests.- 14.1 Introduction.- 14.2 The New Bayesian-Frequentist Test.- 14.3 Normal Testing.- 14.4 The "Two-Sided" Normal Test With Shifted Conjugate Prior.- 14.5 The "Two-Sided" Test With Uniform Prior.- 14.6 Lower Bound on ? .- 14.7
Springer Book Archives