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Nonparametric comparison of regression curves - an empirical process approach

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  • Dette, Holger
  • Neumeyer, Natalie

Abstract

We propose a new test for the comparison of two regression curves, which is based on a difference of two marked empirical processes based on residuals. The large sample behaviour of the corresponding statistic is studied to provide a full nonparametric comparison of regression curves. In contrast to most procedures suggested in the literature the new procedure is applicable in the case of different design points and heteroscedasticity. Moreover, it is demonstrated that the proposed test detects continuous alternatives converging to the null at a rate N-1/2. In the case of equal design points the fundamental statistic reduces to a test statistic proposed by Delgado (1993) and therefore resembles in spirit classical goodness-of-fit tests. As a byproduct we explain the problems of a related test proposed by Kulasekera (1995) and Kulasekera and Wang (1997) with respect to accuracy in the approximation of the level. These difficulties mainly originate from the comparison with the quantiles of an inappropriate limit distribution. A simulation study is conducted to investigate the finite sample properties of a wild bootstrap version of the new tests.

Suggested Citation

  • Dette, Holger & Neumeyer, Natalie, 2000. "Nonparametric comparison of regression curves - an empirical process approach," Technical Reports 2000,62, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200062
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    References listed on IDEAS

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    1. Delgado, Miguel A., 1993. "Testing the equality of nonparametric regression curves," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 199-204, June.
    2. King, Eileen & Hart, Jeffrey D. & Wehrly, Thomas E., 1991. "Testing the equality of two regression curves using linear smoothers," Statistics & Probability Letters, Elsevier, vol. 12(3), pages 239-247, September.
    3. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
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