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Testing independence in nonparametric regression

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  • Neumeyer, Natalie
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    Abstract

    We propose a new test for independence of error and covariate in a nonparametric regression model. The test statistic is based on a kernel estimator for the L2-distance between the conditional distribution and the unconditional distribution of the covariates. In contrast to tests so far available in literature, the test can be applied in the important case of multivariate covariates. It can also be adjusted for models with heteroscedastic variance. Asymptotic normality of the test statistic is shown. Simulation results and a real data example are presented.

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    File URL: http://www.sciencedirect.com/science/article/B6WK9-4VJ03S7-1/2/3d8ceed0b96473178dfed9c51003c827
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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 100 (2009)
    Issue (Month): 7 (August)
    Pages: 1551-1566

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    Handle: RePEc:eee:jmvana:v:100:y:2009:i:7:p:1551-1566

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    Related research

    Keywords: Bootstrap Goodness-of-fit Kernel estimator Nonparametric regression Test for independence;

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Einmahl, J.H.J. & Keilegom, I. van, 2008. "Tests for independence in nonparametric regression," Open Access publications from Tilburg University urn:nbn:nl:ui:12-192434, Tilburg University.
    2. Einmahl, J.H.J. & Keilegom, I. van, 2008. "Specification tests in nonparametric regression," Open Access publications from Tilburg University urn:nbn:nl:ui:12-192435, Tilburg University.
    3. Müller Ursula U. & Schick Anton & Wefelmeyer Wolfgang, 2007. "Estimating the error distribution function in semiparametric regression," Statistics & Risk Modeling, De Gruyter, vol. 25(1/2007), pages 18, January.
    4. Ingrid Keilegom & Wenceslao González Manteiga & César Sánchez Sellero, 2008. "Goodness-of-fit tests in parametric regression based on the estimation of the error distribution," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 17(2), pages 401-415, August.
    5. 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.
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    Citations

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    Cited by:
    1. Simos Meintanis, 2013. "Comments on: 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, vol. 22(3), pages 432-436, September.
    2. Florens, Jean-Pierre & Simar, Léopold & Van Keilegom, Ingrid, 2014. "Frontier estimation in nonparametric location-scale models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 456-470.
    3. Hlávka, Zdenek & Husková, Marie & Meintanis, Simos G., 2011. "Tests for independence in non-parametric heteroscedastic regression models," Journal of Multivariate Analysis, Elsevier, vol. 102(4), pages 816-827, April.
    4. Ingrid Van Keilegom, 2013. "Comments on: 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, vol. 22(3), pages 428-431, September.

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