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Testing independence in nonparametric regression

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  • Neumeyer, Natalie

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.

Suggested Citation

  • Neumeyer, Natalie, 2009. "Testing independence in nonparametric regression," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1551-1566, August.
  • Handle: RePEc:eee:jmvana:v:100:y:2009:i:7:p:1551-1566
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    References listed on IDEAS

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    1. Einmahl, John H.J. & Van Keilegom, Ingrid, 2008. "Specification tests in nonparametric regression," Journal of Econometrics, Elsevier, vol. 143(1), pages 88-102, March.
    2. P. M. Robinson, 1991. "Consistent Nonparametric Entropy-Based Testing," Review of Economic Studies, Oxford University Press, vol. 58(3), pages 437-453.
    3. Einmahl, J.H.J. & van Keilegom, I., 2006. "Tests for Independence in Nonparametric Regression," Discussion Paper 2006-80, Tilburg University, Center for Economic Research.
    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;Sociedad de Estadística e Investigación Operativa, 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.
    6. 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 1-18, January.
    7. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
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    Citations

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    Cited by:

    1. 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.
    2. 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;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 432-436, September.
    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. Jun Zhang & Zhenghui Feng & Peirong Xu, 2015. "Estimating the conditional single-index error distribution with a partial linear mean regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 61-83, March.
    5. repec:eee:ecmode:v:69:y:2018:i:c:p:134-149 is not listed on IDEAS
    6. Simar, Léopold & Vanhems, Anne & Van Keilegom, Ingrid, 2016. "Unobserved heterogeneity and endogeneity in nonparametric frontier estimation," Journal of Econometrics, Elsevier, vol. 190(2), pages 360-373.
    7. Holger Dette & Matthias Guhlich & Natalie Neumeyer, 2015. "Testing for additivity in nonparametric quantile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(3), pages 437-477, June.
    8. 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;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 428-431, September.
    9. repec:eee:csdana:v:122:y:2018:i:c:p:135-155 is not listed on IDEAS

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