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

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