ROBUST HIERARCHICAL BAYES ESTIMATION OF SMALL-AREA CHARACTERISTICS INTHE PRESENCE OF COVARIATES AND OUTLIERS

A robust hierarchical Bayes method is developed to smooth small area m eans when a number of covariates are available. The method is particul arly suited when one or more outliers are present in the data. It is w ell known that the regular Bayes estimators of small. area means, unde r normal prior distribution, perform poorly in presence of even one ex treme observation. In this case the Bayes estimators collapse to the d irect survey estimators. This paper introduces a general theory for ro bust hierarchical Bayes estimation procedure using a fairly rich class of scale mixtures of normal prior distributions. To retain maximum be nefit from combining information from related sources, we suggest to u se Cauchy prior distribution for the outlying areas and an appropriate scale mixture of normal prior whose tail is lighter than the Cauchy p rior for the rest of the areas. It is shown that, unlike the hierarchi cal Bayes estimator under a normal prior, our estimator has more prote ction against outlying observations. (C) 1995 Academic Press, Inc.