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The Smooth Colonel Meets the Reverend

Author

Listed:
  • Kiefer, Nicholas M.

    (Cornell U and CREATES, The Danish Science Foundation, U of Aarhus)

  • Racine, Jeffrey S.

    (McMaster U)

Abstract

Kernel smoothing techniques have attracted much attention and some notoriety in recent years. The attention is well deserved as kernel methods free researchers from having to impose rigid parametric structure on their data. The notoriety arises from the fact that the amount of smoothing (i.e., local averaging) that is appropriate for the problem at hand is under the control of the researcher. In this paper we provide a deeper understanding of kernel smoothing methods for discrete data by leveraging the unexplored links between hierarchical Bayesmodels and kernelmethods for discrete processes. A number of potentially useful results are thereby obtained, including bounds on when kernel smoothing can be expected to dominate non-smooth (e.g., parametric) approaches in mean squared error and suggestions for thinking about the appropriate amount of smoothing.

Suggested Citation

  • Kiefer, Nicholas M. & Racine, Jeffrey S., 2008. "The Smooth Colonel Meets the Reverend," Working Papers 08-01, Cornell University, Center for Analytic Economics.
    • Handle: RePEc:ecl:corcae:08-01
    as

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    File URL: https://cae.economics.cornell.edu/08-01.pdf
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    References listed on IDEAS

    as
    1. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
    2. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    3. Ouyang, Desheng & Li, Qi & Racine, Jeffrey S., 2009. "Nonparametric Estimation Of Regression Functions With Discrete Regressors," Econometric Theory, Cambridge University Press, vol. 25(1), pages 1-42, February.
    4. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355, December.
    5. Li, Qi & Racine, Jeff, 2003. "Nonparametric estimation of distributions with categorical and continuous data," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 266-292, August.
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    Cited by:

    1. Daniel Wikström, 2015. "A finite sample improvement of the fixed effects estimator applied to technical inefficiency," Journal of Productivity Analysis, Springer, vol. 43(1), pages 29-46, February.
    2. Qi Li & Juan Lin & Jeffrey S. Racine, 2013. "Optimal Bandwidth Selection for Nonparametric Conditional Distribution and Quantile Functions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 57-65, January.
    3. Nicholas M. Kiefer & Jeffrey S. Racine, 2017. "The smooth colonel and the reverend find common ground," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 241-256, March.
    4. Li, Qi & Maasoumi, Esfandiar & Racine, Jeffrey S., 2009. "A nonparametric test for equality of distributions with mixed categorical and continuous data," Journal of Econometrics, Elsevier, vol. 148(2), pages 186-200, February.

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