On a nonparametric test for linear relationships

Holger Dette

Statistics & Probability Letters, 2000, vol. 46, issue 3, 307-316

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.

Keywords: Model; checking; Nonparametric; regression; Pseudolikelihood; ratio; test; Residuals; Testing; linearity (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (1)

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