Improved prediction in finite population sampling using convex combination of parametric and non-parametric models

Abstract

We consider inference for sampling from a finite population when information on auxiliary variables is available. In such situations it is well known that both model based and model assisted approaches perform better than the purely design-based approach provided the assumed model that links study variable and auxiliary variables is appropriate. An approach based on non-parametric regression is robust against model specification and performs well when the sample size is large. However, for small to medium sample sizes a parametric model-based or model-assisted approach performs better even if the assumed parametric model is not the correct one. In this paper, we propose a compromise approach that considers a convex combination of a parametric and a non-parametric model where the weight for the parametric model is determined based on its adequacy. We determine the optimal weight by minimizing the cross-validation based prediction error. We illustrate the use of this idea in the case of the stratified simple random sampling design and the probability proportional to size sampling design. Using simulations, we show that our approach provides predictions that are better than both the purely parametric model based and the purely non-parametric model based predictions.