A martingale-transform goodness-of-fit test for the form of the conditional variance - Holger Dette; Benjamin Hetzler (Technische Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen, 2008)
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 Cramer-von-Mises functionals. The finite sample properties of the proposed tests are investigated by means of a simulation study.
Keywords: 519; nonparametric regression; goodness-of-it test; martingale transform; conditional variance