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

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

2008-09-29

arxiv.org/abs/0809.4914v1

Mathematics

Statistics Theory

24 pages,

Scientific paper

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 Cram\'{e}r-von-Mises functionals. The finite sample properties of the proposed tests are investigated by means of a simulation study.

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