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Dette, Holger
Hetzler, Benjamin
Year of Publication: 
Series/Report no.: 
Technical Report // Sonderforschungsbereich 475, Komplexitätsreduktion in Multivariaten Datenstrukturen, Universität Dortmund 2008,07
In the common nonparametric regression model the problem of testing for a specific parametric form of the variance function is considered. Recently Dette and Hetzler (2008) proposed a test statistic, which is based on an empirical process of pseudo residuals. The process converges weakly to a Gaussian process with a complicated covariance kernel depending on the data generating process. In the present paper we consider a standardized version of this process and propose a martingale transform to obtain asymptotically distribution free tests for the corresponding Kolmogorov-Smirnov and Cramœer-von-Mises functionals. The finite sample properties of the proposed tests are investigated by means of a simulation study.
nonparametric regression
goodness-of-it test
martingale transform
conditional variance
Document Type: 
Working Paper

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