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Biometrika Advance Access published online on May 23, 2007
Biometrika, doi:10.1093/biomet/asm035
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Copyright © 2007 Biometrika Trust

Article

Resampling-based empirical prediction: an appliction to small area estimation

Soumendra N. Lahiri and Tapabrata Maiti

Department of Statistics, Iowa State University, Ames, Iowa 50011, U.S.A.

Myron Katzoff and Van Parsons

National Center for Health Statistics, 3311 Toledo Road, Hyattsville, Maryland 20782, U.S.A.

snlahiri{at}iastate.edu

taps{at}iastate.edu

mjk5{at}cdc.gov

vlp1{at}cdc.gov

Received for publication 1 March 2005. Revision received 1 September 2006.
  Abstract

Best linear unbiased prediction is well known for its wide range of applications including small area estimation. While the theory is well established for mixed linear models and under normality of the error and mixing distributions, the literature is sparse for nonlinear mixed models under nonnormality of the error distribution or of the mixing distributions. We develop a resampling-based unified approach for predicting mixed effects under a generalized mixed model set-up. Second-order-accurate nonnegative estimators of mean squared prediction errors are also developed. Given the parametric model, the proposed methodology automatically produces estimators of the small area parameters and their mean squared prediction errors, without requiring explicit analytical expressions for the mean squared prediction errors.

Key Words: Best predictor • Bootstrap • Kernel • Mean squared prediction error


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