Analysis of variance in nonparametric regression models

In a nonparametric regression model with a multivariate explanatory variabl e we consider the problem of testing the hypothesis that specific interacti ons in a canonical decomposition of the model vanish. A simple consistent t est is developed which is bared on the difference between the corresponding sum of squares of the ordinary ANOVA for the multi-factor case and a nonpa rametric variance estimator. This presents an analogue of the classical ANO VA in the nonparametric regression setup. Asymptotic normality of the intro duced test statistic is derived under the null hypothesis and under fixed a lternatives. The finite sample behaviour of the proposed procedures is illu strated by a small simulation study and a data example. (C) 2001 Academic P ress.