Conditional Akaike information under covariate shift with application to small area estimation

TL;DR

This paper develops a variable selection criterion based on conditional Akaike information for linear mixed models under covariate shift, with applications to small area estimation and demonstrated through simulations.

Contribution

It introduces a new criterion for variable selection under covariate shift, specifically tailored for small area estimation, and validates its effectiveness through simulations.

Findings

The proposed criterion improves variable selection accuracy under covariate shift.

Simulation results show better predictive performance compared to existing methods.

Application to real land price data demonstrates practical usefulness.

Abstract

In this study, we consider the problem of selecting explanatory variables of fixed effects in linear mixed models under covariate shift, which is when the values of covariates in the model for prediction differ from those in the model for observed data. We construct a variable selection criterion based on the conditional Akaike information introduced by Vaida and Blanchard (2005). We focus especially on covariate shift in small area estimation and demonstrate the usefulness of the proposed criterion. In addition, numerical performance is investigated through simulations, one of which is a design-based simulation using a real dataset of land prices.