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On a nonparametric test for linear relationships

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  • Dette, Holger

Abstract

In a recent paper Azzalini and Bowman (1993, J. Roy. Statist. Soc. Ser. B 55, 549-559) proposed a pseudolikelihood ratio test for checking the linearity in a homoscedastic nonparametric regression model under a fixed design assumption. In this paper, we study the asymptotic properties of this test and establish asymptotic normality under the hypothesis of linearity and under any fixed alternative with different rates of convergence in both cases. In a second part of the paper these results are extended to nonparmetric regression models with a random design.

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  • Dette, Holger, 2000. "On a nonparametric test for linear relationships," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 307-316, February.
    • Handle: RePEc:eee:stapro:v:46:y:2000:i:3:p:307-316
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    References listed on IDEAS

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    1. H. Dette & A. Munk, 1998. "Testing heteroscedasticity in nonparametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(4), pages 693-708.
    2. 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.
    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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    Cited by:

    1. Biedermann, Stefanie & Dette, Holger, 2001. "Optimal designs for testing the functional form of a regression via nonparametric estimation techniques," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 215-224, April.

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