Small Area Estimation / Edition 1

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Overview

"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, March 2004 on the First Edition)

An accessible introduction and much-needed guide to indirect estimation methods, both traditional and model-based, in the form of small area estimation. Readers will also find the latest methods for measuring the variability of the estimates as well as the techniques for model validation.

Written by an accomplished team of 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, 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.
Emphasis is on real data throughout the book. More than two dozen new topics have been added to this edition (such as 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) along with selected R subroutines.

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Editorial Reviews

From the Publisher
"...impressive and elegantly written...maintains a high level of mathematical rigour and depth...lucid, self-contained and well-organized..." (Zentralblatt Math, Vol. 1026, 2004)

“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, March 2004)

"The book is a systematic and economical account of the development of the subject by one of its foremost contributors.” (Short Book Reviews, 2003)

"This book will help to advance the subject and be a valuable resource for practitioners and theorists.” (Statistics in Transition, November 2003)

"This book is essential to any basic library on small estimation. Both theoretical researchers and practitioners in this subject will certainly appreciate the themes treated in Rao's book.” (Journal of Official Statistics, 2003)

"...a textbook on small area estimation, probably the only one presently available on this topic...easy to read and each chapter is illustrated by practical examples." (Mathematical Reviews, 2003j)

“...an authoritative and comprehensive account of methods for producing small area estimates by using not conventional direct estimates, but indirect, model-dependent estimates...” (Quarterly of Applied Mathematics, Vol. LXI, No. 3, September 2003)

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Product Details

Meet 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.

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Table of Contents

List of Figures viii

List of Tables x

Foreword xii

Preface xv

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 Modi_ed 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 35

3.3 Composite Estimation 58

3.4 James-Stein Method 64

3.5 Proofs 73

4 Small Area Models 77

4.1 Introduction 77

4.2 Basic Area Level Model 78

4.3 Basic Unit Level Model 80

4.4 Extensions: Area Level Models 83

4.5 Extensions: Unit Level Models 90

4.6 Generalized Linear Mixed Models 94

5 Empirical Best Linear Unbiased Prediction: Theory 99

5.1 Introduction 99

5.2 General Linear Mixed Model 100

5.3 Block Diagonal Covariance Structure 110

5.4 Model Identi_cation and Checking 113

5.5 Software 120

5.6 Proofs 121

6 EBLUP: Basic Area Level Model 125

6.1 EBLUP estimation 125

6.2 MSE Estimation 138

6.3 Robust estimation in the presence of outliers 148

6.4 Practical issues 150

6.5 Software 172

7 Basic Unit Level Model 175

7.1 EBLUP estimation 175

7.2 MSE Estimation 181

7.3 Applications 188

7.4 Outlier robust EBLUP estimation 195

7.5 M-quantile regression 202

7.6 Practical Issues 207

7.7 Software 229

7.8 Proofs 233

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 249

8.5 Two-fold Subarea Level Models 252

8.6 Multivariate Nested Error Regression Model 253

8.7 Two-fold Nested Error Regression Model 255

8.8 Two-level Model 259

8.9 Models for Multinomial Counts 261

8.10 EBLUP for Vectors of Area Proportions 263

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 _nite population parameters 289

9.5 Binary Data 298

9.6 Disease Mapping 309

9.7 Design-weighted EB estimation: exponential family models 314

9.8 Triple-goal Estimation 317

9.9 Empirical Linear Bayes 320

9.10 Constrained LB 325

9.11 Software 326

9.12 Proofs 331

10 Hierarchical Bayes (HB) Method 335

10.1 Introduction 335

10.2 MCMC Methods 336

10.3 Basic Area Level Model 349

10.4 Unmatched Sampling and Linking Area Level Models 359

10.5 Basic Unit Level Model 364

10.6 General ANOVA Model 371

10.7 HB estimation of general _nite population parameters 372

10.8 Two-level Models 377

10.9 Time Series and Cross-sectional Models 380

10.10 Multivariate Models 385

10.11 Disease Mapping Models 386

10.12 Two-part Nested Error Model 391

10.13 Binary Data 392

10.14 Missing Binary Data 401

10.15 Natural Exponential Family Models 402

10.16 Constrained HB 403

10.17 Approximate HB Inference and Data Cloning 404

10.18 Proofs 405

References 409

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