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Influence functions and robust Bayes and empirical Bayes small area estimation
Department of Statistics, University of Florida, Gainesville, Florida 32611-8545, U.S.A. ghoshm{at}stat.ufl.edu
Department of Statistics, Iowa State University, Ames, Iowa 50011-1210, U.S.A. taps{at}iastate.edu
Department of Statistics, University of Nebraska-Lincoln, Lincoln, Nebraska 68583-0963, U.S.A. aroy2{at}unlnotes.unl.edu
Received for publication 1 November 2005. Revision received 1 April 2008.
We introduce new robust small area estimation procedures based on area-level models. We first find influence functions corresponding to each individual area-level observation by measuring the divergence between the posterior density functions of regression coefficients with and without that observation. Next, based on these influence functions, properly standardized, we propose some new robust Bayes and empirical Bayes small area estimators. The mean squared errors and estimated mean squared errors of these estimators are also found. A small simulation study compares the performance of the robust and the regular empirical Bayes estimators. When the model variance is larger than the sample variance, the proposed robust empirical Bayes estimators are superior.
Key Words: Hellinger distance • Kullback–Leibler divergence • Limited translation rule • Maximum likelihood estimation • Predictive influence function
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