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Nonparametric analysis of covariance

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  • Dette, Holger
  • Neumeyer, Natalie

Abstract

In the problem of testing the equality of k regression curves from independent samples we discuss three methods using nonparametric estimation techniques of the regression function. The first test is based on a linear combination of estimators for the integrated variance function in the individual samples and in the combined sample. The second approach transfers the classical one-way analysis of variance to the situation of comparing nonparametric curves, while the third test compares the differences between the estimates of the individual regression functions by means of an L2-distance. We prove asymptotic normality of all considered statistics under the null hypothesis local and fixed alternatives with different rates corresponding to the various cases. Additionally consistency of a wild bootstrap version of the tests is established. In contrast to most of the procedures proposed in the literature the methods introduced in this paper are also applicable in the case of different design points in each sample and heteroscedastic errors. A simulation study is conducted to investigate the finite sample properties of the new tests and a comparison with recently proposed and related procedures is performed.

Suggested Citation

  • Dette, Holger & Neumeyer, Natalie, 2000. "Nonparametric analysis of covariance," Technical Reports 2000,42, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200042
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    References listed on IDEAS

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    1. Stefanie Biedermann & Holger Dette, 2000. "Testing linearity of regression models with dependent errors by kernel based methods," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 417-438, December.
    2. W. González-Manteiga & R. Cao, 1993. "Testing the hypothesis of a general linear model using nonparametric regression estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 2(1), pages 161-188, December.
    3. Delgado, Miguel A., 1993. "Testing the equality of nonparametric regression curves," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 199-204, June.
    4. Biedermann, Stefanie & Dette, Holger, 2000. "Testing linearity of regression models with dependent errors by kernel based methods," Technical Reports 2000,40, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    5. 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.
    6. Alcalá, J. T. & Cristóbal, J. A. & González-Manteiga, W., 1999. "Goodness-of-fit test for linear models based on local polynomials," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 39-46, March.
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