Large scale sample surveys are usually designed to produce reliable estimates of various characteristics of interest for large geographic areas. However, for effective planning of health, social, and other services, there is a growing demand to produce similar estimates for smaller geographic areas and subpopulations, commonly referred to as small-areas (or small-domains). The accuracy of small-area statistics is especially crucial when data are used to apportion government funds among various groups.
Traditional design-based estimators are not well suited in small-area estimation since they are generally based on a few observations available from the sample survey. Various indirect estimators which combine sample survey data in conjunction with relevant census and administrative data have been considered in the small-area literature. They all use either implicit or explicit models which connect various sources of relevant information.
In this talk, we consider a robust jackknife method to estimate the mean squared error (MSE) of an empirical best predictor (EBP) in a small-area context. The method is valid for a very general class of mixed models and a fairly general class of M-estimators of the model parameters. For the special case of mixed linear model, the method only requires posterior linearity assumption in order to obtain the jackknife MSE estimator of EBLUP (which is also EBP) of a mixed effect. Thus, the proposed jackknife method is more robust than the existing methods which are mostly based on the assumption of normality. A Monte Carlo simulation study supports our theoretical results.