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Title:Nonparametric Analysis of Covariance : the Case of Inhomogeneous and Heteroscedastic Noise PDF Logo
Authors:Scholz, Achim
Neumeyer, Natalie
Munk, Axel
Issue Date:2004
Series/Report no.:Technical Report / Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen 2004,28
Abstract:The purpose of this paper is to propose a procedure for testing the equality of several regression curves fi 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 fi. 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.
Subjects:nonparametric regression
wild bootstrap
Document Type:Working Paper
Appears in Collections:Technical Reports, SFB 475: Komplexitätsreduktion in multivariaten Datenstrukturen, TU Dortmund

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