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Testing independence of covariates and errors in nonparametric regression

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  • Sankar, Subhra
  • Bergsma, Wicher
  • Dassios, Angelos

Abstract

Consider a nonparametric regression model Y = m(X)+✏, where m is an unknown regression function, Y is a real-valued response variable, X is a real co-variate, and ✏ is the error term. In this article, we extend the usual tests for homoscedasticity by developing consistent tests for independence between X and ✏. Further, we investigate the local power of the proposed tests using Le Cam’s contiguous alternatives. An asymptotic power study under local alternatives along with extensive finite sample simulation study shows the performance of the new tests is competitive with existing ones. Furthermore, the practicality of the new tests is shown using two real data sets.

Suggested Citation

  • Sankar, Subhra & Bergsma, Wicher & Dassios, Angelos, 2017. "Testing independence of covariates and errors in nonparametric regression," LSE Research Online Documents on Economics 83780, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:83780
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    References listed on IDEAS

    as
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    4. 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.
    5. Anne Leucht & Michael Neumann, 2013. "Degenerate $$U$$ - and $$V$$ -statistics under ergodicity: asymptotics, bootstrap and applications in statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(2), pages 349-386, April.
    6. Neumeyer, Natalie, 2009. "Testing independence in nonparametric regression," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1551-1566, August.
    7. Einmahl, J.H.J. & van Keilegom, I., 2006. "Tests for Independence in Nonparametric Regression," Other publications TiSEM 0c6f2c43-aa7d-45c1-9d43-7, Tilburg University, School of Economics and Management.
    8. Babu, G. Jogesh & Rao, C. Radhakrishna, 1988. "Joint asymptotic distribution of marginal quantiles and quantile functions in samples from a multivariate population," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 15-23, October.
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    More about this item

    Keywords

    asymptotic power; contiguous alternatives; distance covariance; kendall’s tau; nonparametric regression model; measure of association;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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