Robust Empirical Best Small Area Finite Population Mean Estimation Using a Mixture Model

Abstract

We propose a new robust empirical best estimation approach to estimate small area finite population means that are relatively insensitive to a model misspecification or to the presence of outliers. This important robustness property is achieved by replacing the standard normality assumption of the sampling errors in a nested-error regression (NER) model by a scale mixture of two normal distributions with different variances. We present a formal statistical test to identify if a small area is an outlier and provide an efficient new computing algorithm to implement our procedure. We examine the finite sample robustness properties of our proposed method using a Monte Carlo simulation and compare the proposed method with alternative existing methods in a study using data from the Current Employment Statistics (CES) survey conducted by the US Bureau of Labor Statistics (BLS).