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A Correction to "Generalized Nonparametric Smoothing with Mixed Discrete and Continuous Data" by Li, Simar & Zelenyuk (2014, CSDA)

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  • Jeffrey S. Racine

Abstract

Li & Racine (2004) have proposed a nonparametric kernel-based method for smoothing in the presence of categorical predictors as an alternative to the classical nonparametric approach that splits the data into subsets (‘cells’) defined by the unique combinations of the categorical predictors. Li, Simar & Zelenyuk (2014) present an alternative to Li & Racine’s (2004) method that they claim possesses lower mean square error and generalizes and improves upon the existing approaches. However, these claims do not appear to withstand scrutiny. A number of points need to be brought to the attention of practitioners, and two in particular stand out; a) Li et al.’s (2014) own simulation results reveal that their estimator performs worse than the existing classical ‘split’ estimator and appears to be inadmissible, and b) the claim that Li et al.’s (2014) estimator dominates that of Li & Racine (2004) on mean square error grounds does not appear to be the case. The classical split estimator and that of Li & Racine (2004) are both consistent, and it will be seen that Li & Racine’s (2004) estimator remains the best all around performer. And, as a practical matter, Li et al.’s (2014) estimator is not a feasible alternative in typical settings involving multinomial and multiple categorical predictors.

Suggested Citation

  • Jeffrey S. Racine, 2016. "A Correction to "Generalized Nonparametric Smoothing with Mixed Discrete and Continuous Data" by Li, Simar & Zelenyuk (2014, CSDA)," Department of Economics Working Papers 2016-01, McMaster University.
  • Handle: RePEc:mcm:deptwp:2016-01
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    File URL: http://socserv.mcmaster.ca/econ/rsrch/papers/archive/2016-01.pdf
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    References listed on IDEAS

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    1. Li, Degui & Simar, Léopold & Zelenyuk, Valentin, 2016. "Generalized nonparametric smoothing with mixed discrete and continuous data," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 424-444.
    2. QI Li & Desheng Ouyang & Jeffrey S. Racine, 2013. "Categorical semiparametric varying‐coefficient models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(4), pages 551-579, June.
    3. Valentin Zelenyuk & Leopold Simar, 2011. "To Smooth or Not to Smooth? The Case of Discrete Variables in Nonparametric Regressions," CEPA Working Papers Series WP102011, School of Economics, University of Queensland, Australia.
    4. Shujie Ma & Jeffrey S. Racine & Lijian Yang, 2015. "Spline Regression in the Presence of Categorical Predictors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(5), pages 705-717, August.
    5. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
    6. Li, Qi & Racine, Jeffrey S., 2010. "Smooth Varying-Coefficient Estimation And Inference For Qualitative And Quantitative Data," Econometric Theory, Cambridge University Press, vol. 26(6), pages 1607-1637, December.
    7. Subodh Kumar & R. Robert Russell, 2002. "Technological Change, Technological Catch-up, and Capital Deepening: Relative Contributions to Growth and Convergence," American Economic Review, American Economic Association, vol. 92(3), pages 527-548, June.
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    Keywords

    Kernel regression; cross-validation; finite-sample performance; replication.;

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