Estimation of mean squared error of model-based small area estimators

Estimation of small area means under a basic area level model is studied, using an empirical Bayes (best) estimator or a weighted estimator with fixed weights. Mean squared errors (MSEs) of the estimators and nearly unbiased (or exactly unbiased) estimators of MSE are derived under three different approaches: design based (approach 1), unconditional model based (approach 2) and conditional model based (approach 3). Performance of MSE estimators under the three approaches with respect to relative bias and coefficient of variation is also studied, using a simulation experiment.