The Residual Information Criterion, Corrected

Abstract

Shi and Tsai (JRSSB, 2002) proposed an interesting residual information criterion (RIC) for model selection in regression. Their RIC was motivated by the principle of minimizing the Kullback-Leibler discrepancy between the residual likelihoods of the true and candidate model. We show, however, under this principle, RIC would always choose the full (saturated) model. The residual likelihood therefore, is not appropriate as a discrepancy measure in defining information criterion. We explain why it is so and provide a corrected residual information criterion as a remedy.