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new test for the parametric form of the variance function in nonparametric regression

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  • Dette, Holger
  • van Keilegom, Ingrid

Abstract

In the common nonparametric regression model the problem of testing for the parametric form of the conditional variance is considered. A stochastic process based on the difference between the empirical processes obtained from the standardized nonparametric residuals under the null hypothesis (of a specific parametric form of the variance function) and the alternative is introduced and its weak convergence established. This result is used for the construction of a Cramer von Mises type statistic for testing the parametric form of the conditional variance. The finite sample properties of a bootstrap version of this test are investigated by means of a simulation study. In particular the new procedure is compared with some of the currently available methods for this problem and its performance is illustrated by means of a data example.

Suggested Citation

  • Dette, Holger & van Keilegom, Ingrid, 2005. "new test for the parametric form of the variance function in nonparametric regression," Technical Reports 2005,32, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200532
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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. Diblasi, Angela & Bowman, Adrian, 1997. "Testing for constant variance in a linear model," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 95-103, April.
    3. Koul, H. L. & Lahiri, S. N., 1994. "On Bootstrapping M-Estimated Residual Processes in Multiple Linear-Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 49(2), pages 255-265, May.
    4. Michael G. Akritas & Ingrid Van Keilegom, 2001. "Non‐parametric Estimation of the Residual Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 549-567, September.
    5. Breusch, T S & Pagan, A R, 1979. "A Simple Test for Heteroscedasticity and Random Coefficient Variation," Econometrica, Econometric Society, vol. 47(5), pages 1287-1294, September.
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