Variable selection by stepwise slicing in nonparametric regression

We consider variable selection issue 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 tests of hypotheses as opposed to existing methods in the literature. Asymptotic properties are examined and empirical results are given.