Nonparametric Analysis of Covariance - the Case of Inhomogeneous and Heteroscedastic Noise

Abstract

The purpose of this paper is to propose a procedure for testing the equality of several regression curves f_i in nonparametric regression models when the noise is inhomogeneous. This extends work of Dette and Neumeyer (2001) and it is shown that the new test is asymptotically uniformly more powerful. The presented approach is very natural because it transfers the maximum likelihood statistic from a heteroscedastic one way ANOVA to the context of nonparametric regression. The maximum likelihood estimators will be replaced by kernel estimators of the regression functions f_i. It is shown that the asymptotic distribution of the obtained test statistic is nuisance parameter free. Finally, for practical purposes a bootstrap variant is suggested. In a simulation study, level and power of this test will be briefly investigated. In summary, our theoretical findings are supported by this study.