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

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  • Biedermann, Stefanie
  • Dette, Holger

Abstract

In a recent paper Gonzalez Manteiga and Vilar Fernandez (1995) considered the problem of testing linearity of a regression under MA structure of the errors using a weighted L1-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 Bow_ man (1993) Zheng (1996) and Dette (1999) to the case of non-independent errors and compares these methods with the method of Gonzalez Manteiga and Vilar Fernandez (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.

Suggested Citation

  • Biedermann, Stefanie & Dette, Holger, 2000. "Testing linearity of regression models with dependent errors by kernel based methods," Technical Reports 2000,40, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200040
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    File URL: https://www.econstor.eu/bitstream/10419/77303/2/2000-40.pdf
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    References listed on IDEAS

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    1. Alcalá, J. T. & Cristóbal, J. A. & González-Manteiga, W., 1999. "Goodness-of-fit test for linear models based on local polynomials," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 39-46, March.
    2. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
    3. Gonzalez Manteiga, W. & Vilar Fernandez, J. M., 1995. "Testing linear regression models using non-parametric regression estimators when errors are non-independent," Computational Statistics & Data Analysis, Elsevier, vol. 20(5), pages 521-541, November.
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    Cited by:

    1. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    2. Andrea Meilán-Vila & Jean D. Opsomer & Mario Francisco-Fernández & Rosa M. Crujeiras, 2020. "A goodness-of-fit test for regression models with spatially correlated errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 728-749, September.
    3. Bücher, Axel & Dette, Holger & Wieczorek, Gabriele, 2011. "Testing model assumptions in functional regression models," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1472-1488, November.
    4. Zhang, Rongmao & Chan, Ngai Hang & Chi, Changxiong, 2023. "Nonparametric testing for the specification of spatial trend functions," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    5. Anouar El Ghouch & Marc G. Genton & Taoufik Bouezmarni, 2013. "Measuring the Discrepancy of a Parametric Model via Local Polynomial Smoothing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 455-470, September.
    6. Dette, Holger & Neumeyer, Natalie, 2000. "Nonparametric analysis of covariance," Technical Reports 2000,42, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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