Prediction Theory for Finite Populations

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.

Synopsis.- 1. Basic Ideas and Principles.- 1.1. The Fixed Finite Population Model.- 1.2. The Superpopulation 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.- 2.4. Stein-Type Shrinkage Predictors.- 2.5. Exercises.- 3. Bayes and Minimax Predictors.- 3.1. The Multivariate Normal Model.- 3.2. Bayes Linear Predictors.- 3.3. Minimax and Admissible Predictors.- 3.4. Dynamic Bayesian Prediction.- 3.5. Empirical Bayes Predictors.- 3.6. Exercises.- 4. Maximum-Likelihood Predictors.- 4.1. Predictive Likelihoods.- 4.2. Maximum Likelihood Predictors of T Under the Normal Superpopulation Model.- 4.3. Maximum-Likelihood Predictors of the Population Variance Sy2 Under the Normal Regression Model.- 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.- 6.6. Exercises.- 7. Models with Measurement Errors.- 7.1. The Location and Simple Regression Models.- 7.2. Bayesian Models with Measurement Errors.- 7.3. Exercises.- 8. Asymptotic Properties in Finite Populations.- 8.1. Predictors of T.- 8.2. The Asymptotic Distribution of $${hat beta _{{s_k}}}$$.- 8.3. The Linear Regression Model with Measurement Errors.- 8.4. Exercises.- 9. DesignCharacteristics 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.