Estimation of mean squared error of model-based estimators of small area means under a nested error linear regression model

Most of the research on small area estimation has focused on unconditional mean squared error (MSE) estimation under an assumed small area model. Datta et al. (2011) [3] studied conditional MSE estimation of a small area mean under a basic area-level model, conditional on the area-specific direct estimator. In this paper, estimation of a small area mean under a nested error linear regression model is studied, using an empirical best (or Bayes) estimator or a weighted estimator with fixed weights. We derive second-order approximations to unconditional MSE and conditional MSE given the area-specific data and obtain associated second-order correct MSE estimators. The performance of MSE estimators is studied using a simulation experiment as well as a real dataset.