Dette, HolgerHetzler, Benjamin2008-11-262008-11-262008-11-26http://hdl.handle.net/2003/2587010.17877/DE290R-14287In the common nonparametric regression model the problem of testing for a specific para- metric 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 Cramer-von-Mises functionals. The finite sample properties of the proposed tests are investigated by means of a simulation study.enConditional varianceGoodness-of-fit testMartingale transformNonparametric regression004report