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Praise for the First Edition "This pioneering work, in which Rao provides a comprehensive and up-to-date treatment of small area estimation, will become a classic...I believe that it has the potential to turn small area estimation...into a larger area of importance to both researchers and practitioners." Journal of the American Statistical Association Written by two experts in the field, Small Area Estimation, Second Edition provides a comprehensive and up-to-date account of the methods and theory of small area estimation (SAE), particularly indirect estimation based on explicit small area linking models. The model-based approach to small area estimation offers several advantages including increased precision, the derivation of "optimal" estimates and associated measures of variability under an assumed model, and the validation of models from the sample data. Emphasizing real data throughout, the Second Edition maintains a self-contained account of crucial theoretical and methodological developments in the field of SAE. The new edition provides extensive accounts of new and updated research, which often involves complex theory to handle model misspecifications and other complexities. Including information on survey design issues and traditional methods employing indirect estimates based on implicit linking models, Small Area Estimation, Second Edition also features: * Additional sections describing the use of R code data sets for readers to use when replicating applications * Numerous examples of SAE applications throughout each chapter, including recent applications in U.S. Federal programs * New topical coverage on extended design issues, synthetic estimation, further refinements and solutions to the Fay-Herriot area level model, basic unit level models, and spatial and time series models * A discussion of the advantages and limitations of various SAE methods for model selection from data as well as comparisons of estimates derived from models to reliable values obtained from external sources, such as previous census or administrative data Small Area Estimation, Second Edition is an excellent reference for practicing statisticians and survey methodologists as well as practitioners interested in learning SAE methods. The Second Edition is also an ideal textbook for graduate-level courses in SAE and reliable small area statistics.
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Table of Contents

List of Figures xv List of Tables xvii Foreword to the First Edition xix Preface to the Second Edition xxiii Preface to the First Edition xxvii 1 *Introduction 1 1.1 What is a Small Area? 1 1.2 Demand for Small Area Statistics, 3 1.3 Traditional Indirect Estimators, 4 1.4 Small Area Models, 4 1.5 Model-Based Estimation, 5 1.6 Some Examples, 6 2 Direct Domain Estimation 9 2.1 Introduction, 9 2.2 Design-Based Approach, 10 2.3 Estimation of Totals, 11 2.4 Domain Estimation, 16 2.5 Modified GREG Estimator, 21 2.6 Design Issues, 23 2.7 *Optimal Sample Allocation for Planned Domains, 26 2.8 Proofs, 32 3 Indirect Domain Estimation 35 3.1 Introduction, 35 3.2 Synthetic Estimation, 36 3.3 Composite Estimation, 57 3.4.1 Common Weight, 63 3.5 Proofs, 71 4 Small Area Models 75 4.1 Introduction, 75 4.2 Basic Area Level Model, 76 4.3 Basic Unit Level Model, 78 4.4 Extensions: Area Level Models, 81 4.5 Extensions: Unit Level Models, 88 4.6 Generalized Linear Mixed Models, 92 5 Empirical Best Linear Unbiased Prediction (EBLUP): Theory 97 5.1 Introduction, 97 5.2 General Linear Mixed Model, 98 5.3 Block Diagonal Covariance Structure, 108 5.4 *Model Identification and Checking, 111 5.5 *Software, 118 6 Empirical Best Linear Unbiased Prediction (EBLUP): Basic Area Level Model 123 6.1 EBLUP Estimation, 123 6.2 MSE Estimation, 136 6.3 *Robust Estimation in the Presence of Outliers, 146 6.4 *Practical Issues, 148 6.5 *Software, 169 7 Basic Unit Level Model 173 7.1 EBLUP Estimation, 173 7.2 MSE Estimation, 179 7.3 *Applications, 186 7.4 *Outlier Robust EBLUP Estimation, 193 7.5 *M-Quantile Regression, 200 7.6 *Practical Issues, 205 7.7 *Software, 227 7.8 *Proofs, 231 8 EBLUP: Extensions 235 8.1 *Multivariate Fay-Herriot Model, 235 8.2 Correlated Sampling Errors, 237 8.3 Time Series and Cross-Sectional Models, 240 8.4 *Spatial Models, 248 8.5 *Two-Fold Subarea Level Models, 251 8.6 *Multivariate Nested Error Regression Model, 253 8.7 Two-Fold Nested Error Regression Model, 254 8.8 *Two-Level Model, 259 8.9 *Models for Multinomial Counts, 261 8.10 *EBLUP for Vectors of Area Proportions, 262 8.11 *Software, 264 9 Empirical Bayes (EB) Method 269 9.1 Introduction, 269 9.2 Basic Area Level Model, 270 9.3 Linear Mixed Models, 287 9.4 *EB Estimation of General Finite Population Parameters, 289 9.5 Binary Data, 298 9.6 Disease Mapping, 308 9.7 *Design-Weighted EB Estimation: Exponential Family Models, 313 9.8 Triple-Goal Estimation, 315 9.9 Empirical Linear Bayes, 319 9.10 Constrained LB, 324 9.11 *Software, 325 9.12 Proofs, 330 10 Hierarchical Bayes (HB) Method 333 10.1 Introduction, 333 10.2 MCMC Methods, 335 10.3 Basic Area Level Model, 347 10.4 *Unmatched Sampling and Linking Area Level Models, 356 10.5 Basic Unit Level Model, 362 10.6 General ANOVA Model, 368 10.7 *HB Estimation of General Finite Population Parameters, 369 10.8 Two-Level Models, 374 10.9 Time Series and Cross-Sectional Models, 377 10.10 Multivariate Models, 381 10.11 Disease Mapping Models, 383 10.12 *Two-Part Nested Error Model, 388 10.13 Binary Data, 389 10.14 *Missing Binary Data, 397 10.15 Natural Exponential Family Models, 398 10.16 Constrained HB, 399 10.17 *Approximate HB Inference and Data Cloning, 400 10.18 Proofs, 402 References 405 Author Index 431 Subject Index 437

About the Author

J. N. K. Rao, PhD, is Professor Emeritus and Distinguished Research Professor in the School of Mathematics and Statistics, Carleton University, Ottawa, Canada. He is an editorial advisor for the Wiley Series in Survey Methodology. Isabel Molina, PhD, is Associate Professor of Statistics at Universidad Carlos III de Madrid, Spain.

Reviews

"The book is an excellent reference for practicing statisticians and survey methodologists as well as practitioners interested in learning SAE methods. The second edition is also an ideal textbook for graduate-level courses in SAE and reliable small area statistics." (Zentralblatt MATH 2016) The book is an excellent reference for practicing statisticians and survey methodologists as well as practitioners interested in learning SAE methods. The second edition is also an ideal textbook for graduate-level courses in SAE and reliable small area statistics.

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