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Testing for symmetric error distribution in nonparametric regression models

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  • Neumeyer, Natalie
  • Dette, Holger

Abstract

For the problem of testing symmetry of the error distribution in a nonparametric regression model we propose as a test statistic the difference between the two empirical distribution functions of estimated residuals and their counterparts with opposite signs. The weak convergence of the difference process to a Gaussian process is shown. The covariance structure of this process depends heavily on the density of the error distribution, and for this reason the performance of a symmetric wild bootstrap procedure is discussed in asymptotic theory and by means of a simulation study. In contrast to the available procedures the new test is also applicable under heteroscedasticity.

Suggested Citation

  • Neumeyer, Natalie & Dette, Holger, 2003. "Testing for symmetric error distribution in nonparametric regression models," Technical Reports 2003,11, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200311
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    References listed on IDEAS

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    1. Hyndman, R.J. & Yao, Q., 1998. "Nonparametric Estimation and Symmetry Tests for Conditional Density Functions," Monash Econometrics and Business Statistics Working Papers 17/98, Monash University, Department of Econometrics and Business Statistics.
    2. Koziol, James A., 1985. "A note on testing symmetry with estimated parameters," Statistics & Probability Letters, Elsevier, vol. 3(4), pages 227-230, July.
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    Cited by:

    1. Delgado, Miguel A. & Carlos Escanciano, J., 2007. "Nonparametric tests for conditional symmetry in dynamic models," Journal of Econometrics, Elsevier, vol. 141(2), pages 652-682, December.

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