A new minimum contrast approach for inference in single-index models

Semiparametric single-index models represent an appealing compromise between parametric and nonparametric approaches and have been widely investigated in the literature. The underlying assumption in single-index models is that the information carried by the vector of covariates could be summarized by a one-dimensional projection. We propose a new, general inference approach for such models, based on a quadratic form criterion involving kernel smoothing. The approach could be applied with general single-index assumptions, in particular for mean regression models and conditional law models. The covariates could be unbounded and no trimming is necessary. A resampling method for building confidence intervals for the index parameter is proposed. Our empirical experiments reveal that the new method performs well in practice.