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On a nonparametric test for linear relationships

✍ Scribed by Holger Dette

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 108 KB
Volume: 46
Category: Article
ISSN: 0167-7152
DOI: 10.1016/s0167-7152(99)00130-3

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✦ Synopsis

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 ÿxed 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 ÿxed alternative with di erent 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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