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.

Keywords:

• kernel smoothing
• cross-validation
• AIC
• semiparametric family

Acknowledgements

We thank the referees for very helpful comments. Our thanks also go to Mr John Box for proof reading and correcting the English in this paper. This research is supported by the Singapore National Research Foundation under its Cooperative Basic Research Grant and administered by the Singapore Ministry of Healths National Medical Research Council (Grant No. NMRC/CBRG/0014/2012) and the Hong Kong GRF Grant (Grant No. HKBU201610)