Information criteria for Fay–Herriot model selection

The selection of an appropriate model is a fundamental step of the data analysis in small area estimation. Bias corrections to the Akaike information criterion, AICAIC, and to the Kullback symmetric divergence criterion, KICKIC, are derived for the Fay–Herriot model. Furthermore, three bootstrap-corrected variants of AICAIC and of KICKIC are proposed. The performance of the eight considered criteria is investigated with a simulation study and an application to real data. The obtained results suggest that there are better alternatives than the classical AICAIC.