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Probabilistic characterization of directional distances and their robust versions

  • Simar, Léopold
  • Vanhems, Anne

In this work, we analyze the performance of production units using the directional distance function which allows to measure the distance to the frontier of the production set along any direction in the inputs/outputs space. We show that this distance can be expressed as a simple transformation of radial or hyperbolic distance. This formulation allows to define robust directional distances in the lines of α-quantile or order-m partial frontiers and also conditional directional distance functions, conditional to environmental factors. We propose simple methods of estimation and derive the asymptotic properties of our estimators.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 166 (2012)
Issue (Month): 2 ()
Pages: 342-354

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Handle: RePEc:eee:econom:v:166:y:2012:i:2:p:342-354
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. Badin, Luiza & Daraio, Cinzia & Simar, Léopold, 2010. "Optimal bandwidth selection for conditional efficiency measures: A data-driven approach," European Journal of Operational Research, Elsevier, vol. 201(2), pages 633-640, March.
  2. Fare, Rolf, et al, 1993. "Derivation of Shadow Prices for Undesirable Outputs: A Distance Function Approach," The Review of Economics and Statistics, MIT Press, vol. 75(2), pages 374-80, May.
  3. Kneip, Alois & Simar, Léopold & Wilson, Paul W., 2008. "Asymptotics And Consistent Bootstraps For Dea Estimators In Nonparametric Frontier Models," Econometric Theory, Cambridge University Press, vol. 24(06), pages 1663-1697, December.
  4. Florens, Jean-Pierre & Simar, Leopold, 2005. "Parametric approximations of nonparametric frontiers," Journal of Econometrics, Elsevier, vol. 124(1), pages 91-116, January.
  5. Sushama Murty & R. Robert Russell & Steven B. Levkoff, 2011. "On modeling pollution-generating technologies," Discussion Papers 1101, Exeter University, Department of Economics.
  6. Daouia, Abdelaati & Simar, Leopold, 2007. "Nonparametric efficiency analysis: A multivariate conditional quantile approach," Journal of Econometrics, Elsevier, vol. 140(2), pages 375-400, October.
  7. Gregoriou, Greg N. & Sedzro, Komlan & Zhu, Joe, 2005. "Hedge fund performance appraisal using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 164(2), pages 555-571, July.
  8. Cinzia Daraio & Leopold Simar, 2003. "Introducing Environmental Variables in Nonparametric Frontier Models: a Probabilistic Approach," LEM Papers Series 2003/17, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  9. Fare, Rolf & Grosskopf, Shawna & Noh, Dong-Woon & Weber, William, 2005. "Characteristics of a polluting technology: theory and practice," Journal of Econometrics, Elsevier, vol. 126(2), pages 469-492, June.
  10. Jeong, Seok-Oh & Simar, Léopold, 2006. "Linearly interpolated FDH efficiency score for nonconvex frontiers," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2141-2161, November.
  11. Léopold Simar & Paul Wilson, 2011. "Inference by the m out of n bootstrap in nonparametric frontier models," Journal of Productivity Analysis, Springer, vol. 36(1), pages 33-53, August.
  12. 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.
  13. David C. Wheelock & Paul Wilson, 2007. "Non-parametric, unconditional quantile estimation for efficiency analysis with an application to Federal Reserve check processing operations," Working Papers 2005-027, Federal Reserve Bank of St. Louis.
  14. Daraio, Cinzia & Simar, Leopold, 2006. "A robust nonparametric approach to evaluate and explain the performance of mutual funds," European Journal of Operational Research, Elsevier, vol. 175(1), pages 516-542, November.
  15. 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.
  16. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
  17. Michael C. Jensen, 1968. "The Performance Of Mutual Funds In The Period 1945–1964," Journal of Finance, American Finance Association, vol. 23(2), pages 389-416, 05.
  18. Rolf Färe & Shawna Grosskopf, 2000. "Theory and Application of Directional Distance Functions," Journal of Productivity Analysis, Springer, vol. 13(2), pages 93-103, March.
  19. Morey, Matthew R. & Morey, Richard C., 1999. "Mutual fund performance appraisals: a multi-horizon perspective with endogenous benchmarking," Omega, Elsevier, vol. 27(2), pages 241-258, April.
  20. Léopold Simar, 2003. "Detecting Outliers in Frontier Models: A Simple Approach," Journal of Productivity Analysis, Springer, vol. 20(3), pages 391-424, November.
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