## Prediction Theory for Finite Populations / by Heleno Bolfarine, Shelemyahu Zacks (Springer Series in Statistics)

データ種別 電子ブック New York, NY : Springer New York 1992 英語 XII, 207 p : online resource

EB0067836

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内容注記 Synopsis1. Basic Ideas and Principles1.1. The Fixed Finite Population Model1.2. The Superpopulation Model1.3. Predictors of Population Quantities1.4. The Model—Based Design—Based Approach1.5. Exercises2. Optimal Predictors of Population Quantities2.1. Best Linear Unbiased Predictors2.2. Best Unbiased Predictors2.3. Equivariant Predictors2.4. Stein—Type Shrinkage Predictors2.5. Exercises3. Bayes and Minimax Predictors3.1. The Multivariate Normal Model3.2. Bayes Linear Predictors3.3. Minimax and Admissible Predictors3.4. Dynamic Bayesian Prediction3.5. Empirical Bayes Predictors3.6. Exercises4. Maximum—Likelihood Predictors4.1. Predictive Likelihoods4.2. Maximum Likelihood Predictors of T Under the Normal Superpopulation Model4.3. Maximum—Likelihood Predictors of the Population Variance Sy2 Under the Normal Regression Model4.4. Exercises5. Classical and Bayesian Prediction Intervals5.1. Confidence Prediction Intervals5.2. Tolerance Prediction Intervals for T5.3. Bayesian Prediction Intervals5.4. Exercises6. The Effects of Model Misspecification, Conditions For Robustness, and Bayesian Modeling6.1. Robust Linear Prediction of T6.2. Estimation of the Prediction Variance6.3. Simulation Estimates of the ?* MSE of $${\hat T_R}$$6.4. Bayesian Robustness6.5. Bayesian Modeling6.6. Exercises7. Models with Measurement Errors7.1. The Location and Simple Regression Models7.2. Bayesian Models with Measurement Errors7.3. Exercises8. Asymptotic Properties in Finite Populations8.1. Predictors of T8.2. The Asymptotic Distribution of $${\hat \beta _{{s_k}}}$$8.3. The Linear Regression Model with Measurement Errors8.4. Exercises9. Design Characteristics of Predictors9.1. The QR Class of Predictors9.2. ADU Predictors9.3. Optimal ADU Predictors9.4. ExercisesGlossary of PredictorsAuthor Index 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 LCSH:MathematicsLCSH:Applied mathematicsLCSH:Engineering mathematicsFREE:MathematicsFREE:Applications of Mathematics DC23:519 ISBN:9781461229049 9781461229049