Analysis of Variance in Nonparametric Regression Models

In a nonparametric regression model with a multivariate explanatory variable we consider the problem of testing the hypothesis that specific interactions in a canonical decomposition of the model vanish. A simple consistent test is developed which is based on the difference between the corresponding sum of squares of the ordinary ANOVA for the multi-factor case and a nonparametric variance estimator. This presents an analogue of the classical ANOVA in the nonparametric regression setup. Asymptotic normality of the introduced test statistic is derived under the null hypothesis and under fixed alternatives. The finite sample behaviour of the proposed procedures is illustrated by a small simulation study and a data example.