An ANOVA-type nonparametric diagnostic test for heteroscedastic regression models

Abstract

For the heteroscedastic nonparametric regression model Y _ni =m (x _ni )+σ (x _ni ) ε _ni , i=1, …, n, we discuss a novel method for testing some parametric assumptions about the regression function m. The test is motivated by recent developments in the asymptotic theory for analysis of variance when the number of factor levels is large. Asymptotic normality of the test statistic is established under the null hypothesis and suitable local alternatives. The similarity of the form of the test statistic to that of the classical F-statistic in analysis of variance allows easy and fast calculation. Simulation studies demonstrate that the new test possesses satisfactory finite-sample properties.

Keywords:

• heteroscedastic errors
• lack-of-fit tests
• local alternatives
• nearest neighbourhood; nonparametric regression