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A new test for the parametric form of the variance function in non-parametric regression

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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.

Keywords: Bootstrap; Kernel estimation; Non-parametric regression; Residual distribution; Testing heteroscedasticity; Testing homoscedasticity

Document Type: Research Article

DOI: http://dx.doi.org/10.1111/j.1467-9868.2007.00616.x

Affiliations: 1: Ruhr-Universität Bochum, Germany 2: Universität Hamburg, Germany 3: Université catholique de Louvain, Belgium

Publication date: November 1, 2007

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