Mean squared error estimators of small area means using survey weights

Using survey weights [You & Rao You and Rao The Canadian Journal of Statistics 2002 30 431-439] proposed a pseudo-empirical best linear unbiased prediction (pseudo EBLUP) estimator of a small area mean under a nested error linear regression model This estimator borrows strength across ire is through a linking model and makes use of survey weights to ensure design consistency and preserve benchmarking property in the sense that the estimators add up to a reliable direct estimator of the mean of a large area covering the small areas In this article a second order approximation to the mean squared error (MSE) of the pseudo EBLUP estimator of a small area mean is derived Using this approximation an estimator of MSE that is nearly unbiased is derived the MSE estimator of You & Rao [You and Rao The Canadian Journal of Statistics 2002 30 431-439] ignored cross-product terms in the MSE and hence it is based Empirical results on the performance of the proposed MSE estimator are also presented The Canadian Journal of Statistics 38 598-608 2010 (C) 2010 Statistical Society or Canada