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.


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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.

Item Type: Article
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Keywords: test of linearity, nonparametric regression, moving average process, optimal weighted least squares, asymptotic relative efficiency
Organisations: Statistics
ePrint ID: 41840
Date :
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Date Deposited: 10 Oct 2006
Last Modified: 16 Apr 2017 18:57
Further Information:Google Scholar
URI: http://eprints.soton.ac.uk/id/eprint/41840

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