Variable Selection by Stepwise Slicing in Nonparametric Regression

In this paper, variable selection issue is considered in a nonparametric regression setting. Two stepwise procedures based on variance estimators are proposed for selecting the significant variables in a general nonparametric regression model. These procedures do not require multidimensional smoothing at intermediate steps and they are based on formal rests of hypotheses as opposed to existing methods in the literature. Asymptotic properties are examined and empirical results are given.