A new test for the parametric form of the variance function in non-parametric regression
Source: Journal of the Royal Statistical Society: Series B (Statistical Methodology), Volume 69, Number 5, November 2007 , pp. 903-917(15)
In the common non-parametric 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 that are obtained from the standardized non-parametric 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 Kolmogorov–Smirnov and a Cramér–von Mises type of statistic for testing the parametric form of the conditional variance. The consistency of a bootstrap approximation is established, and the finite sample properties of this approximation 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.
Document Type: Research Article
Publication date: November 2007