Estimation of Finite Population Domain Means

Abstract

In this article we introduce a general methodology for producing a model-assisted empirical best predictor (EBP) of a finite population domain mean using data from a complex survey. Our method improves on the commonly used design-consistent survey estimator by using a suitable mixed model. Such a model combines information from related sources, such as census and administrative data. Unlike a purely model-based EBP, the proposed model-assisted EBP converges in probability to the customary design-consistent estimator as the domain and sample sizes increase. The convergence in probability is shown to hold with respect to the sampling design, irrespective of the assumed mixed model, a property commonly known as design consistency. This property ensures robustness of the proposed predictor against possible model failures. In addition, the convergence in probability is shown to be valid with respect to the assumed mixed model (model consistency). A new mean squared prediction error (MSPE) estimator is proposed. Unlike earlier MSPE estimators, our MSPE estimator is second-order unbiased. Our simulation results demonstrate the robustness properties of our proposed model-assisted predictor and the usefulness of the second-order unbiased MSPE estimator.