Robust Model-Based and Model-Assisted Predictors of the Finite Population Total

Abstract

The prediction approach to finite population inference has received considerable attention in recent years. Under this approach, the finite population is assumed to be a realization from a superpopulation described by a known probability model, usually a linear model. The prediction approach is often criticized for its lack of robustness against model misspecification. In this article we revisit this important issue and introduce a new robust prediction approach in which the superpopulation model is chosen adaptively from the well-known Box–Cox class of probability distributions. The richness of the Box–Cox class ensures robustness in our model-based prediction approach. We explain how our robust model-based predictor can be adjusted to handle zero observations for the study variable and to achieve the design-unbiasedness and benchmarking properties. We demonstrate the robustness of our proposed predictors using a Monte Carlo simulation study and a real life example.