Single-Index Model Selections
Biometrika, 2001

in this paper, Professors Prasad Naik and Chih-Ling Tsai derive a new model selection criterion for single-index models, AIC, by minimizing the expected Kullback-Leibler distances between the true and candidate models.

The pro-posed 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 unifies approach to model selection across both parametric and nonparametric functions. Monte Carlo studies demonstrate that AIC performs satisfactorily in most situations.

The authors illustrate the practical use of AIC with an empirical example for modeling the hedonic price function for cars. In addition, we extend the applicability of AIC to partially linear and additive single-index models.