  This article considers a robust hierarchical Bayesian approach to deal with
random effects of small area means when some of these effects assume extreme
values, resulting in outliers. In presence of outliers, the standard
Fay-Herriot model, used for modeling area-level data, under normality
assumptions of the random effects may overestimate random effects variance,
thus provides less than ideal shrinkage towards the synthetic regression
predictions and inhibits borrowing information. Even a small number of
substantive outliers of random effects result in a large estimate of the random
effects variance in the Fay-Herriot model, thereby achieving little shrinkage
to the synthetic part of the model or little reduction in posterior variance
associated with the regular Bayes estimator for any of the small areas. While a
scale mixture of normal distributions with known mixing distribution for the
random effects has been found to be effective in presence of outliers, the
solution depends on the mixing distribution. As a possible alternative solution
to the problem, a two-component normal mixture model has been proposed based on
noninformative priors on the model variance parameters, regression coefficients
and the mixing probability. Data analysis and simulation studies based on real,
simulated and synthetic data show advantage of the proposed method over the
standard Bayesian Fay-Herriot solution derived under normality of random
effects.
