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Testing additivity by kernel based methods - what is a reasonable test?

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  • Dette, Holger
  • von Lieres und Wilkau, Carsten

Abstract

In the common nonparametric regression model with high dimensional predictor several tests for the hypothesis of an additive regression are investigated. The corresponding test statistics are either based on the diiferences between a fit under the assumption of additivity and a fit in the general model or based on residuals under the assumption of additivity. For all tests asymptotic normality is established under the null hypothesis of additivity and under fixed alternatives with different rates of convergence corresponding to both cases. These results are used for a comparison of the different methods. It is demonstrated that a statistic based on an empirical L1 - distance of the Nadaraya Watson and the marginal integration estimator yields the asymptotically most efficient procedure if these are compared with respect to the asymptotic behaviour under fixed alternatives.

Suggested Citation

  • Dette, Holger & von Lieres und Wilkau, Carsten, 2000. "Testing additivity by kernel based methods - what is a reasonable test?," Technical Reports 2000,39, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200039
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    References listed on IDEAS

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    2. Härdle, Wolfgang & Chen, R., 1995. "Estimation and Variable Selection in Additive Nonparametric Regression Models," SFB 373 Discussion Papers 1995,16, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    3. 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.
    4. 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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    Cited by:

    1. Dette, Holger & von Lieres und Wilkau, Carsten & Sperlich, Stefan, 2001. "A comparison of different nonparametric methods for inference on additive models," Technical Reports 2001,22, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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