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A smooth nonparametric conditional quantile frontier estimator

  • Martins-Filho, Carlos
  • Yao, Feng

Traditional estimators for nonparametric frontier models (DEA, FDH) are very sensitive to extreme values/outliers. Recently, Aragon et al. [2005. Nonparametric frontier estimation: a conditional quantile-based approach. Econometric Theory 21, 358-389] proposed a nonparametric [alpha]-frontier model and estimator based on a suitably defined conditional quantile which is more robust to extreme values/outliers. Their estimator is based on a nonsmooth empirical conditional distribution. In this paper, we propose a new smooth nonparametric conditional quantile estimator for the [alpha]-frontier model. Our estimator is a kernel based conditional quantile estimator that builds on early work of Azzalini [1981. A note on the estimation of a distribution function and quantiles by a kernel method. Biometrika 68, 326-328]. It is computationally simple, resistant to outliers and extreme values, and smooth. In addition, the estimator is shown to be consistent and asymptotically normal under mild regularity conditions. We also show that our estimator's variance is smaller than that of the estimator proposed by Aragon et al. A simulation study confirms the asymptotic theory predictions and contrasts our estimator with that of Aragon et al.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 143 (2008)
Issue (Month): 2 (April)
Pages: 317-333

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Handle: RePEc:eee:econom:v:143:y:2008:i:2:p:317-333
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. Greene, William H., 1990. "A Gamma-distributed stochastic frontier model," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 141-163.
  2. Christensen, Laurits R & Greene, William H, 1976. "Economies of Scale in U.S. Electric Power Generation," Journal of Political Economy, University of Chicago Press, vol. 84(4), pages 655-76, August.
  3. Hall, Peter & Park, Byeong U. & Stern, Steven E., 1998. "On Polynomial Estimators of Frontiers and Boundaries," Journal of Multivariate Analysis, Elsevier, vol. 66(1), pages 71-98, July.
  4. Li, Qi & Racine, Jeffrey S, 2008. "Nonparametric Estimation of Conditional CDF and Quantile Functions With Mixed Categorical and Continuous Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 423-434.
  5. Park, B.U. & Simar, L. & Weiner, Ch., 2000. "The Fdh Estimator For Productivity Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 16(06), pages 855-877, December.
  6. Cazals, Catherine & Florens, Jean-Pierre & Simar, Leopold, 2002. "Nonparametric frontier estimation: a robust approach," Journal of Econometrics, Elsevier, vol. 106(1), pages 1-25, January.
  7. Martins-Filho, Carlos & Yao, Feng, 2007. "Nonparametric frontier estimation via local linear regression," Journal of Econometrics, Elsevier, vol. 141(1), pages 283-319, November.
  8. Aragon, Y. & Daouia, A. & Thomas-Agnan, C., 2005. "Nonparametric Frontier Estimation: A Conditional Quantile-Based Approach," Econometric Theory, Cambridge University Press, vol. 21(02), pages 358-389, April.
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