A martingale-transform goodness-of-fit test for the form of the conditional variance

H. Dette; B. Hetzler

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arXiv · 0809.4914

A martingale-transform goodness-of-fit test for the form of the conditional variance

H. Dette·B. Hetzler

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Abstract

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 Cramér-von-Mises functionals. The finite sample properties of the proposed tests are investigated by means of a simulation study.

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H. Dette, B. Hetzler. 2008-09-29. A martingale-transform goodness-of-fit test for the form of the conditional variance. https://arxiv.org/abs/0809.4914

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