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Small Area Estimation

Small Area Estimation

J. N. K. Rao

ISBN: 978-0-471-72218-2

Feb 2005

344 pages

Select type: O-Book

Description

An accessible introduction to indirect estimation methods, both traditional and model-based. Readers will also find the latest methods for measuring the variability of the estimates as well as the techniques for model validation.
  • Uses a basic area-level linear model to illustrate the methods
  • Presents the various extensions including binary response data through generalized linear models and time series data through linear models that combine cross-sectional and time series features
  • Provides recent applications of SAE including several in U.S. Federal programs
  • Offers a comprehensive discussion of the design issues that impact SAE
List of Figures.

List of Tables.

Foreword.

Preface.

1. Introduction.

What is a Small Area?

Demand for Small Area Statistics.

Traditional Indirect Estimators.

Small Area Models.

Model-Based Estimation.

Some Examples.

2. Direct Domain Estimation.

Introduction.

Design-based Approach.

Estimation of Totals.

Domain Estimation.

Modified Direct Estimators.

Design Issues.

Proofs.

3. Traditional Demographic Methods.

Introduction.

Symptomatic Accounting Techniques.

Regression Symptomatic Procedures.

Dual-system Estimation of Total Population.

Derivation of Average MSEs.

4. Indirect Domain Estimation.

Introduction.

Synthetic Estimation.

Composite Estimation.

James-Stein Method.

Proofs.

5. Small Area Models.

Introduction.

Basic Area Level (Type A) Mode l.

Basic Unit Level (Type B) Model.

Extensions: Type A Models.

Extensions: Type B Models.

Generalized Linear Mixed Models.

6. Empirical Best Linear Unbiased Prediction: Theory.

Introduction.

General Linear Mixed Model.

Block Diagonal Covariance Structure.

Proofs.

7. EBLUP: Basic Models.

Basic Area Level Model.

Basic Unit Level Model.

8. EBLUP: Extensions.

Multivariate Fay-Herriot Model.

Correlated Sampling Errors.

Time Series and Cross-sectional Models.

Spatial Models.

Multivariate Nested Error Regression Model.

Random Error Variances Linear Model.

Two-fold Nested Error Regression Model.

Two-level Model.

9. Empirical Bayes (EB) Method.

Introduction.

Basic Area Level Model.

Linear Mixed Models.

Binary Data.

Disease Mapping.

Triple-goal Estimation.

Empirical Linear Bayes.

Constrained LB.

Proofs.

10. Hierarchical Bayes (HB) Method.

Introduction.

MCMC Methods.

Basic Area Level Model.

Unmatched Sampling and Linking Area Level Models.

Basic Unit Level Model.

General ANOVA Model.

Two-level Models.

Time Series and Cross-sectional Models.

Multivariate Models.

Disease Mapping Models.

Binary Data.

Exponential Family Models.

Constrained HB.

Proofs.

References.

Author Index.

Subject Index.

"...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)