Testing linearity of regression models with dependent errors by kernel based methods
Testing linearity of regression models with dependent errors by kernel based methods
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.
test of linearity, nonparametric regression, moving average process, optimal weighted least squares, asymptotic relative efficiency
417-438
Biedermann, Stefanie
fe3027d2-13c3-4d9a-bfef-bcc7c6415039
Dette, Holger
8c7b1c2e-3adc-45df-acfc-9e76509a228e
2000
Biedermann, Stefanie
fe3027d2-13c3-4d9a-bfef-bcc7c6415039
Dette, Holger
8c7b1c2e-3adc-45df-acfc-9e76509a228e
Biedermann, Stefanie and Dette, Holger
(2000)
Testing linearity of regression models with dependent errors by kernel based methods.
Test, 9 (2), .
Abstract
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
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Statistics
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Local EPrints ID: 41840
URI: http://eprints.soton.ac.uk/id/eprint/41840
PURE UUID: 12345c53-df6f-4de8-9800-71079537513c
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Date deposited: 10 Oct 2006
Last modified: 16 Mar 2024 03:51
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Author:
Holger Dette
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