Single-index model selections

Abstract

We derive a new model selection criterion for single-index models, AICC, by minimising the expected Kullback-Leibler distance between the true and candidate models. The proposed criterion selects not only relevant variables but also the smoothing parameter for an unknown link function. Thus, it is a general selection criterion that provides a unified approach to model selection across both parametric and nonparametric functions. Monte Carlo studies demonstrate that AICC performs satisfactorily in most situations. We illustrate the practical use of AICC with an empirical example for modelling the hedonic price function for cars. In addition, we extend the applicability of AICC to partially linear and additive single-index models. © 2001 Biomctrika Trust.