Prediction Theory for Finite Populations

ISBN-13: 9781461277132 / Angielski / Miękka / 2011 / 207 str.

Heleno Bolfarine; Shelemyahu Zacks

Opis

A large number of papers have appeared in the last twenty years on estimating and predicting characteristics of finite populations. This monograph is designed to present this modern theory in a systematic and consistent manner. The authors' approach is that of superpopulation models in which values of the population elements are considered as random variables having joint distributions. Throughout, the emphasis is on the analysis of data rather than on the design of samples. Topics covered include: optimal predictors for various superpopulation models, Bayes, minimax, and maximum likelihood predictors, classical and Bayesian prediction intervals, model robustness, and models with measurement errors. Each chapter contains numerous examples, and exercises which extend and illustrate the themes in the text. As a result, this book will be ideal for all those research workers seeking an up-to-date and well-referenced introduction to the subject.

Spis treści

Synopsis.- 1. Basic Ideas and Principles.- 1.1. The Fixed Finite Population Model.- 1.2. The Superpopulation Model.- 1.2.1. The Regression Model.- 1.3. Predictors of Population Quantities.- 1.4. The Model—Based Design—Based Approach.- 1.5. Exercises.- 2. Optimal Predictors of Population Quantities.- 2.1. Best Linear Unbiased Predictors.- 2.2. Best Unbiased Predictors.- 2.3. Equivariant Predictors.- 2.3.1. A General Formulation.- 2.3.2. Location Equivariant Predictors of T Under Model SM1.- 2.3.3. Location Equivariant Predictors of T Under the Regression Model.- 2.3.4. Scale Equivariant Predictors of T.- 2.3.5. Location—Scale Equivariant Predictors of T.- 2.3.6. Location—Scale Equivariant Predictors of Sy2.- 2.4. Stein—Type Shrinkage Predictors.- 2.5. Exercises.- 3. Bayes and Minimax Predictors.- 3.1. The Multivariate Normal Model.- 3.1.1. Bayes Predictors of T.- 3.1.2. Bayes Predictors of ?N.- 3.1.3. Bayes Predictors of Sy2.- 3.2. Bayes Linear Predictors.- 3.3. Minimax and Admissible Predictors.- 3.4. Dynamic Bayesian Prediction.- 3.4.1. The Multinormal Dynamic Model.- 3.4.1.1. Dynamic Prediction of Tt.- 3.4.1.2. Dynamic Prediction of Sty2.- 3.5. Empirical Bayes Predictors.- 3.6. Exercises.- 4. Maximum—Likelihood Predictors.- 4.1. Predictive Likelihoods.- 4.1.1. Estimative Predictive Likelihoods.- 4.1.2. Profile Predictive Likelihoods.- 4.1.3. The Lauritzen—Hinkley Predictive Likelihoods.- 4.1.4. The Royall Predictive Likelihoods.- 4.2. Maximum Likelihood Predictors of T Under the Normal Superpopulation Model.- 4.2.1. Estimative Likelihood Predictors.- 4.2.2. Profile Likelihood Predictors.- 4.2.3. The LH Likelihood Predictors.- 4.2.4. The Royall Maximum—Likelihood Predictors.- 4.3. Maximum—Likelihood Predictors of the Population Variance Sy2 Under the Normal Regression Model.- 4.3.1. Estimative Likelihood Predictors.- 4.3.2. Profile Likelihood Predictors.- 4.3.3. LH Likelihood Predictors.- 4.4. Exercises.- 5. Classical and Bayesian Prediction Intervals.- 5.1. Confidence Prediction Intervals.- 5.2. Tolerance Prediction Intervals for T.- 5.3. Bayesian Prediction Intervals.- 5.4. Exercises.- 6. The Effects of Model Misspecification, Conditions For Robustness, and Bayesian Modeling.- 6.1. Robust Linear Prediction of T.- 6.2. Estimation of the Prediction Variance.- 6.3. Simulation Estimates of the ?* MSE of $${\hat T_R}$$.- 6.4. Bayesian Robustness.- 6.5. Bayesian Modeling.- 6.5.1. The Framework.- 6.5.2. The Normal Linear Model.- 6.6. Exercises.- 7. Models with Measurement Errors.- 7.1. The Location and Simple Regression Models.- 7.1.1. Model SM1.- 7.1.2. Simple Regression Model.- 7.1.3. Regression Type Predictors.- 7.2. Bayesian Models with Measurement Errors.- 7.2.1. Model SM1.- 7.2.2. Model SM6.- 7.2.3. Simple Regression Model.- 7.2.4. Orthogonal Transformations.- 7.3. Exercises.- 8. Asymptotic Properties in Finite Populations.- 8.1. Predictors of T.- 8.2. The Asymptotic Distribution of $${\hat \beta _{}}$$.- 8.3. The Linear Regression Model with Measurement Errors.- 8.4. Exercises.- 9. Design Characteristics of Predictors.- 9.1. The QR Class of Predictors.- 9.2. ADU Predictors.- 9.3. Optimal ADU Predictors.- 9.4. Exercises.- Glossary of Predictors.- Author Index.