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Testing linearity of regression models with dependent errors by kernel based methods

Biedermann, Stefanie and Dette, Holger (2000) Testing linearity of regression models with dependent errors by kernel based methods Test, 9, (2), pp. 417-438.

Record type: Article


In a recent paper González Manteiga and Vilar Fernández (1995) considered the problem of testing linearity of a regression under MA(infinity) structure of the errors using a weighted L2-distance between a parametric and a nonparametric fit. They established asymptotic normality of the corresponding test statistic under the hypothesis and under local alternatives. In the present paper we extend these results and establish asymptotic normality of the statistic under fixed alternatives. This result is then used to prove that the optimal (with respect to uniform maximization of power) weight function in the test of Gonzalez Manteiga and Vilar Fernandez (1995) is given by the Lebesgue measure independently of the design density.
The paper also discusses several extensions of tests proposed by Azzalini and Bowman (1993), Zheng (1996) and Dette (1999) to the case of non-independent errors and compares these methods with the method of González Manteiga and Vilar Fernández (1995). It is demonstrated that among the kernel based methods the approach of the latter authors is the most efficient from an asymptotic point of view.

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Published date: 2000
Keywords: test of linearity, nonparametric regression, moving average process, optimal weighted least squares, asymptotic relative efficiency
Organisations: Statistics


Local EPrints ID: 41840
PURE UUID: 12345c53-df6f-4de8-9800-71079537513c

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Date deposited: 10 Oct 2006
Last modified: 17 Jul 2017 15:27

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Author: Holger Dette

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