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Nonparametric Estimation Of Regression Functions With Discrete Regressors

Author

Listed:
  • Ouyang, Desheng
  • Li, Qi
  • Racine, Jeffrey S.

Abstract

We consider the problem of estimating a nonparametric regression model containing categorical regressors only. We investigate the theoretical properties of least squares cross-validated smoothing parameter selection, establish the rate of convergence (to zero) of the smoothing parameters for relevant regressors, and show that there is a high probability that the smoothing parameters for irrelevant regressors converge to their upper bound values, thereby automatically smoothing out the irrelevant regressors. A small-scale simulation study shows that the proposed cross-validation-based estimator performs well in finite-sample settings.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:etheor:v:25:y:2009:i:01:p:1-42_09
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    Citations

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    Cited by:

    1. repec:wyi:journl:002112 is not listed on IDEAS
    2. Phillip Heiler & Jana Mareckova, 2019. "Shrinkage for Categorical Regressors," Papers 1901.01898, arXiv.org.
    3. Henderson, Daniel J. & Kumbhakar, Subal C. & Li, Qi & Parmeter, Christopher F., 2015. "Smooth coefficient estimation of a seemingly unrelated regression," Journal of Econometrics, Elsevier, vol. 189(1), pages 148-162.
    4. Nicholas Kiefer & Jeffrey Racine, 2009. "The smooth Colonel meets the Reverend," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(5), pages 521-533.
    5. Müller, Ursula U. & Schick, Anton & Wefelmeyer, Wolfgang, 2015. "Estimators in step regression models," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 124-129.
    6. Kaul, Sapna & Boyle, Kevin J. & Kuminoff, Nicolai V. & Parmeter, Christopher F. & Pope, Jaren C., 2013. "What can we learn from benefit transfer errors? Evidence from 20 years of research on convergent validity," Journal of Environmental Economics and Management, Elsevier, vol. 66(1), pages 90-104.
    7. Lien, Donald & Hu, Yue & Liu, Long, 2017. "A note on using ratio variables in regression analysis," Economics Letters, Elsevier, vol. 150(C), pages 114-117.
    8. Nadine McCloud & Christopher F. Parmeter, 2017. "Calculating Degrees of Freedom in Multivariate Local Polynomial Regression," Working Papers 2017-14, University of Miami, Department of Economics.
    9. Alessandro Bonanno & Francesco Bimbo & Marco Costanigro & Alfons Oude Lansink & Rosaria Viscecchia, 2019. "Credence attributes and the quest for a higher price – a hedonic stochastic frontier approach," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 46(2), pages 163-192.
    10. 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.
    11. Heiler, Phillip & Mareckova, Jana, 2021. "Shrinkage for categorical regressors," Journal of Econometrics, Elsevier, vol. 223(1), pages 161-189.
    12. Zongwu Cai & Qi Li, 2013. "Some Recent Develop- ments on Nonparametric Econometrics," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    13. Phillip Heiler, 2020. "Efficient Covariate Balancing for the Local Average Treatment Effect," Papers 2007.04346, arXiv.org.
    14. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.

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