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.

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