"Conditional AIC under Covariate Shift with Application to Small Area Prediction"

In this paper, we consider the problem of selecting explanatory variables of fixed effects in linear mixed models under covariate shift, which is the situation that the values of covariates in the predictive model are different from those in the observed model. We construct a variable selection criterion based on the conditional Akaike information introduced by Vaida and Blanchard (2005) and the proposed criterion is generalization of the conditional Akaike information criterion (conditional AIC) in terms of covariate shift. We especially focus on covariate shift in small area prediction and show usefulness of the proposed criterion through simulation studies.