On Bias-Robust Mean Squared Error Estimation for Pseudo-Linear Small Area Estimators

We discuss bias-robust mean squared error estimation for estimators of finite population domain means that can be expressed in pseudo-linear form, i.e. as weighted sums of sample values. Our approach represents an extension of the ideas in Royall and Cumberland (1978) and appears to lead to estimators that are simpler to implement, and potentially more robust, than those suggested in the small area literature. We illustrate the usefulness of our approach through extensive model-based and design-based simulation, with the latter based on two realistic survey data sets containing small area information.