On bias-robust mean squared error estimation for pseudo-linear small area estimators

We propose a method of mean squared error (MSE) estimation for estimators of finite population domain means that can be expressed in pseudo-linear form, i.e., as weighted sums of sample values. In particular, it can be used for estimating the MSE of the empirical best linear unbiased predictor, the model-based direct estimator and the M-quantile predictor. The proposed method represents an extension of the ideas in Royall and Cumberland (1978) and leads to MSE estimators that are simpler to implement, and potentially more bias-robust, than those suggested in the small area literature. However, it should be noted that the MSE estimators defined using this method can also exhibit large variability when the area-specific sample sizes are very small. We illustrate the performance of the method through extensive model-based and design-based simulation, with the latter based on two realistic survey data sets containing small area information.