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.
Autorentext
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.
Zusammenfassung
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.
Inhalt
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
1.6.1 Health 6
1.6.2 Agriculture 7
1.6.3 Income for Small Places 8
1.6.4 Poverty Counts 8
1.6.5 Median Income of Four-Person Families 8
1.6.6 Poverty Mapping 8
2 Direct Domain Estimation 9
2.1 Introduction 9
2.2 Design-Based Approach 10
2.3 Estimation of Totals 11
2.3.1 Design-Unbiased Estimator 11
2.3.2 Generalized Regression Estimator 13
2.4 Domain Estimation 16
2.4.1 Case of No Auxiliary Information 16
2.4.2 GREG Domain Estimation 17
2.4.3 Domain-Specific Auxiliary Information 18
2.5 Modified GREG Estimator 21
2.6 Design Issues 23
2.6.1 Minimization of Clustering 24
2.6.2 Stratification 24
2.6.3 Sample Allocation 24
2.6.4 Integration of Surveys 25
2.6.5 Dual-Frame Surveys 25
2.6.6 Repeated Surveys 26
2.7 *Optimal Sample Allocation for Planned Domains 26
2.7.1 Case (i) 26
2.7.2 Case (ii) 29
2.7.3 Two-Way Stratification: Balanced Sampling 31
2.8 Proofs 32
2.8.1 Proof of YGR(𝐱) = 𝐗 32
2.8.2 Derivation of Calibration Weights 𝑤j 32
2.8.3 Proof of Y = X^T𝐁^when cj = 𝝂T𝐗j 32
3 Indirect Domain Estimation 35
3.1 Introduction 35
3.2 Synthetic Estimation 36
3.2.1 No Auxiliary Information 36
3.2.2 *Area Level Auxiliary Information 36
3.2.3 *Unit Level Auxiliary Information 37
3.2.4 Regression-Adjusted Synthetic Estimator 42
3.2.5 Estimation of MSE 43
3.2.6 Structure Preserving Estimation 45
3.2.7 *Generalized SPREE 49
3.2.8 *Weight-Sharing Methods 53
3.3 Composite Estimation 57
3.3.1 Optimal Estimator 57
3.3.2 Sample-Size-Dependent Estimators 59
3.4 JamesStein Method 63
3.4.1 Common Weight 63
3.4.2 Equal Variances 𝜓i