new test for the parametric form of the variance function in nonparametric regression - Holger Dette; Ingrid van Keilegom (Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen, 2005)
In the common nonparametric regression model the problem of testing for the parametric form of the conditional variance is considered. A stochastic process based on the difference between the empirical processes obtained from the standardized nonparametric residuals under the null hypothesis (of a specific parametric form of the variance function) and the alternative is introduced and its weak convergence established. This result is used for the construction of a Cramer von Mises type statistic for testing the parametric form of the conditional variance. The finite sample properties of a bootstrap version of this test are investigated by means of a simulation study. In particular the new procedure is compared with some of the currently available methods for this problem and its performance is illustrated by means of a data example.
Keywords: 519; Bootstrap; Kernel estimation; Nonparametric regression; Residual distribution; Testing heteroscedasticity; Testing homoscedasticity; Regression; Nichtparametrisches Verfahren; Statistischer Test; Theorie