Single-index Models

Abstract

The single-index model is a generalization of the linear regression model for which [Image4.gif] where g is an unknown function. This model provides a flexible alternative to the linear regression model while providing more structure than a fully nonparametric approach. In this talk, we first study the properties of partial least squares (PLS) estimators, and compare them in estimating the single-index model to that of sliced inverse regression (SIR). We then derive a model selection criterion, AICC, for single-index models. AICC is a general selection criterion that unifies model selection across both parametric and nonparametric functions. Finally, we obtain score tests to assess three potential misspecifications of the single-index model: heteroscedasticity in the errors, autocorrelation in the errors, and omission of important variables in the linear index. Monte Carlo simulations and several real data sets are presented.