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

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  • Dette, Holger
  • Hetzler, Benjamin

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

Suggested Citation

  • Dette, Holger & Hetzler, Benjamin, 2008. "A martingale-transform goodness-of-fit test for the form of the conditional variance," Technical Reports 2008,07, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200807
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    References listed on IDEAS

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    1. H. Dette & A. Munk, 1998. "Testing heteroscedasticity in nonparametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(4), pages 693-708.
    2. Holger Dette & Natalie Neumeyer & Ingrid Van Keilegom, 2007. "A new test for the parametric form of the variance function in non‐parametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 903-917, November.
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