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A smooth nonparametric conditional quantile frontier estimator

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  • Martins-Filho, Carlos
  • Yao, Feng

Abstract

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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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/jeconom

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References

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  1. Martins-Filho, Carlos & Yao, Feng, 2007. "Nonparametric frontier estimation via local linear regression," Journal of Econometrics, Elsevier, vol. 141(1), pages 283-319, November.
  2. repec:wop:humbsf:1998-9 is not listed on IDEAS
  3. Greene, William H., 1990. "A Gamma-distributed stochastic frontier model," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 141-163.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
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Cited by:
  1. Daniel J. Henderson & John A. List & Daniel L. Millimet & Christopher F. Parmeter & Michael K. Price, 2011. "Empirical Implementation of Nonparametric First-Price Auction Models," NBER Working Papers 17095, National Bureau of Economic Research, Inc.
  2. Kortelainen, Mika, 2008. "Estimation of semiparametric stochastic frontiers under shape constraints with application to pollution generating technologies," MPRA Paper 9257, University Library of Munich, Germany.
  3. Henderson, Daniel J. & List, John A. & Millimet, Daniel L. & Parmeter, Christopher F. & Price, Michael K., 2008. "Imposing Monotonicity Nonparametrically in First-Price Auctions," MPRA Paper 8769, University Library of Munich, Germany.
  4. Wang, Yongqiao & Wang, Shouyang & Dang, Chuangyin & Ge, Wenxiu, 2014. "Nonparametric quantile frontier estimation under shape restriction," European Journal of Operational Research, Elsevier, vol. 232(3), pages 671-678.

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