The connection between cross-validation and Akaike information criterion in a semiparametric family

Abstract

Both Akaike information criterion and cross-validation are important tools in model selection. Stone [(1977), ‘An Asymptotic Equivalence of Choice of Model by Cross-Validation and Akaikes Criterion’, Journal of the Royal Statistical Society, Series B, 39, 44–47] established the equivalence of these two criteria for parametric models. In this paper, we build a similar equivalence for a large semiparametric family.