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Nonparametric Analysis of Covariance : the Case of Inhomogeneous and Heteroscedastic Noise

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  • Scholz, Achim
  • Neumeyer, Natalie
  • Munk, Axel

Abstract

The purpose of this paper is to propose a procedure for testing the equality of several regression curves fi in nonparametric regression models when the noise is inhomogeneous. This extends work of Dette and Neumeyer (2001) and it is shown that the new test is asymptotically uniformly more powerful. The presented approach is very natural because it transfers the maximum likelihood statistic from a heteroscedastic one way ANOVA to the context of nonparametric regression. The maximum likelihood estimators will be replaced by kernel estimators of the regression functions fi. It is shown that the asymptotic distribution of the obtained test statistic is nuisance parameter free. Finally, for practical purposes a bootstrap variant is suggested. In a simulation study, level and power of this test will be briefly investigated. In summary, our theoretical findings are supported by this study.

Suggested Citation

  • Scholz, Achim & Neumeyer, Natalie & Munk, Axel, 2004. "Nonparametric Analysis of Covariance : the Case of Inhomogeneous and Heteroscedastic Noise," Technical Reports 2004,28, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200428
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    References listed on IDEAS

    as
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    5. Weerahandi, Samaradasa, 1987. "Testing Regression Equality with Unequal Variances," Econometrica, Econometric Society, vol. 55(5), pages 1211-1215, September.
    6. Fan, Jianqing & Yao, Qiwei, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
    7. Gørgens, Tue, 2002. "Nonparametric comparison of regression curves by local linear fitting," Statistics & Probability Letters, Elsevier, vol. 60(1), pages 81-89, November.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    nonparametric regression; ANOVA; heteroscedasticity; goodness-of-fit; wild bootstrap; efficacy;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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