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Khmaladze transformation of integrated variance processes with applications to goodness-of-fit testing

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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 [8] 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 an application of the Khmaladze transformation 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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Authors and Affiliations

  1. Ruhr-Universität Bochum, Fakultät für Mathematik, Bochum, Germany

    H. Dette & B. Hetzler

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  1. H. Dette
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  2. B. Hetzler
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Correspondence to H. Dette.

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Dette, H., Hetzler, B. Khmaladze transformation of integrated variance processes with applications to goodness-of-fit testing. Math. Meth. Stat. 18, 97–116 (2009). https://doi.org/10.3103/S106653070902001X

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