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Nonparametric frontier estimation from noisy data

  • SCHWARZ, Maik

    ()

    (Université catholique de Louvain, Institut de Statistique, de Biostatistique et de Sciences Actuarielles, B-1348 Louvain-la-Neuve, Belgium)

  • VAN BELLEGEM, Sébastien

    ()

    (Toulouse School of Economics, France; Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

  • FLORENS, Jean - Pierre

    (Toulouse School of Economics, France)

A new nonparametric estimator of production frontiers is defined and studied when the data set of production units is contaminated by measurement error. The measurement error is assumed to be an additive normal random variable on the input variable, but its variance is unknown. The estimator is a modification of the m-frontier, which necessitates the computation of a consistent estimator of the conditional survival function of the input variable given the output variable. In this paper, the identification and the consistency of a new estimator of the survival function is proved in the presence of additive noise with unknown variance. The performance of the estimator is also studied through simulated data.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2010050.

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Date of creation: 01 Aug 2010
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Handle: RePEc:cor:louvco:2010050
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  1. Schwarz, Maik & Van Bellegem, Sébastien, 2009. "Consistent Density Deconvolution under Partially Known Error Distribution," TSE Working Papers 09-097, Toulouse School of Economics (TSE).
  2. Park, Byeong U. & Sickles, Robin C. & Simar, Leopold, 2003. "Semiparametric-efficient estimation of AR(1) panel data models," Journal of Econometrics, Elsevier, vol. 117(2), pages 279-309, December.
  3. Jérémie Bigot & Sébastien Van Bellegem, 2009. "Log-density Deconvolution by Wavelet Thresholding," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 749-763.
  4. Neumann, Michael H., 2007. "Deconvolution from panel data with unknown error distribution," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1955-1968, November.
  5. Bruno de Borger & Kristiaan Kerstens & Wim Moesen & Jacques Vanneste, 1994. "A non-parametric Free Disposal Hull (FDH) approach to technical efficiency: an illustration of radial and graph efficiency measures and some sensitivity results," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 130(IV), pages 647-667, December.
  6. Johannes, Jan & Van Bellegem, Sébastien & Vanhems, Anne, 2009. "Convergence Rates for III-Posed Inverse Problems with an Unknown Operator," TSE Working Papers 09-030, Toulouse School of Economics (TSE).
  7. Daskovska, Alexandra & Simar, Léopold & Van Bellegem, Sébastien, 2009. "Forecasting the Malmquist Productivity Index," TSE Working Papers 09-048, Toulouse School of Economics (TSE).
  8. Kneip, Alois & Park, Byeong U. & Simar, L opold, 1998. "A Note On The Convergence Of Nonparametric Dea Estimators For Production Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 14(06), pages 783-793, December.
  9. Winfried Pohlmeier & Luc Bauwens & David Veredas, 2007. "High frequency financial econometrics. Recent developments," ULB Institutional Repository 2013/136223, ULB -- Universite Libre de Bruxelles.
  10. Leleu, Herve, 2006. "A linear programming framework for free disposal hull technologies and cost functions: Primal and dual models," European Journal of Operational Research, Elsevier, vol. 168(2), pages 340-344, January.
  11. Simar, Léopold, 2003. "How to Improve the Performances of DEA/FDH Estimators in the Presence of Noise?," SFB 373 Discussion Papers 2003,33, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  12. H. Leleu, 2006. "A linear programming framework for free disposal hull technologies and cost functions: primal and dual models," Post-Print hal-00204497, HAL.
  13. 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.
  14. Seiford, Lawrence M. & Thrall, Robert M., 1990. "Recent developments in DEA : The mathematical programming approach to frontier analysis," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 7-38.
  15. 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.
  16. Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
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