Small Area Estimation Diagnostics: The Case of the Fay–Herriot Model

Leverage and Cook’s distance are some of the most important tools in influence analysis, where the main target is to identify observations that might determine the character of model estimates and predictors. In the small area estimation setup, applied statisticians are interested in tools to identify observations that might influence the variance component and the regression parameter estimates, the empirical best linear unbiased predictor and its mean squared error estimate. For this reason, this paper discusses the leverage matrix, the influence on the mean squared error of the empirical predictor, and a Cook’s Distance of the empirical predictor for the Fay–Herriot model, when the area-random effect variance is estimated by the restricted maximum likelihood method. Further, the validity of this approach is illustrated by means of an application to poverty data.