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Robust Hierarchical Bayes Estimation of Small Area Characteristics in the Presence of Covariates and Outliers

By G. S. Datta and P. Lahiri

Abstract

A robust hierarchical Bayes method is developed to smooth small area means when a number of covariates are available. The method is particularly suited when one or more outliers are present in the data. It is well known that the regular Bayes estimators of small. area means, under normal prior distribution, perform poorly in presence of even one extreme observation. In this case the Bayes estimators collapse to the direct survey estimators. This paper introduces a general theory for robust hierarchical Bayes estimation procedure using a fairly rich class of scale mixtures of normal prior distributions. To retain maximum benefit from combining information from related sources, we suggest to use Cauchy prior distribution for the outlying areas and an appropriate scale mixture of normal prior whose tail is lighter than the Cauchy prior for the rest of the areas. It is shown that, unlike the hierarchical Bayes estimator under a normal prior, our estimator has more protection against outlying observations.

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