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A test for the parametric form of the variance function in a partial linear regression model
Authors:Holger Dette  Mareen Marchlewski
Institution:Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum, Germany
Abstract:We consider the problem of testing for a parametric form of the variance function in a partial linear regression model. A new test is derived, which can detect local alternatives converging to the null hypothesis at a rate n-1/2n-1/2 and is based on a stochastic process of the integrated variance function. We establish weak convergence to a Gaussian process under the null hypothesis, fixed and local alternatives. In the special case of testing for homoscedasticity the limiting process is a scaled Brownian bridge. We also compare the finite sample properties with a test based on an L2L2-distance, which was recently proposed by You and Chen 2005. Testing heteroscedasticity in partially linear regression models. Statist. Probab. Lett. 73, 61–70].
Keywords:Partial linear regression model  Model check  Test for variance function
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