Small Area Estimation

ISBN-13: 9781118735787 / Angielski / Twarda / 2015 / 480 str.

J. N. K. Rao

Opis

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. In addition to the 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 describe an R package for SAE and applications with R data sets that readers can replicate
• Numerous examples of SAE applications throughout the book, 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.

Recenzje

"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.

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

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.

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.

Rao, J. N. K. J. N. K. RAO, PhD, is Professor Emeritus and Disti... więcej >

Udostępnij

Spis treści

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

O autorze

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.

Blurb

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.