Influence analysis in small area estimation

Small area estimation is generally recognized as the pool of methodologies designed for indirect estimation of the population parameters in small domains. Data collected form some well-organized sample surveys, can be effectively utilized to derive direct estimates for large areas, such as administrative districts or regions in national territories. This paper discusses the leverage matrix for the Fay-Herriot area-level model, when the area-random effect variance is estimated either by the restricted maximum likelihood or by the moment method. Leverage and Cook's distance are some of the most important tools in influence analysis, where the main target is to identify observations or groups of observations that might determine the character of model estimates and predictors. In the small area estimation setup, applied statistician are interested in tools to identify observation that might influence the variance component and the regression parameter estimates, the EBLUP and its mean squared error estimate. This paper partially address these issues. We introduce in the present work the leverage matrix for the Fay-Herriot area-level model, when we deal both with a restricted maximun likelihood estimate as well as a moment-based estimate of the random-area effect. The problem of the leverage of observed values on predicted values by the EBLUP arise when we consider that, although we utilize convenient estimates, the latter depend on influential values itself. So the leverage matrix of the model can be affected by influential observations through the estimates of the model variance. Detailed formulae on fixed and random effects leverage matrices are presented.