Nonnegative mean squared prediction error estimation in small area estimation

Abstract

Small area estimation has received enormous attention in recent years due to its wide range of application, particularly in policy making decisions. The variance based on direct sample size of small area estimator is unduly large and there is a need of constructing model based estimator with low mean squared prediction error (MSPE). Estimation of MSPE and in particular the bias correction of MSPE plays the central piece of small area estimation research. In this article, a new technique of bias correction for the estimated MSPE is proposed. It is shown that that the new MSPE estimator attains the same level of bias correction as the existing estimators based on straight Taylor expansion and jackknife methods. However, unlike the existing methods, the proposed estimate of MSPE is always nonnegative. Furthermore, the proposed method can be used for general two-level small area models where the variables at each level can be discrete or continuous and, in particular, be nonnormal.