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Robust nonparametric estimators of monotone boundaries

  • Daouia, Abdelaati
  • Simar, Léopold

This paper revisits some asymptotic properties of the robust nonparametric estimators of order-m and order-[alpha] quantile frontiers and proposes isotonized version of these estimators. Previous convergence properties of the order-m frontier are extended (from weak uniform convergence to complete uniform convergence). Complete uniform convergence of the order-m (and of the quantile order-[alpha]) nonparametric estimators to the boundary is also established, for an appropriate choice of m (and of [alpha], respectively) as a function of the sample size. The new isotonized estimators share the asymptotic properties of the original ones and a simulated example shows, as expected, that these new versions are even more robust than the original estimators. The procedure is also illustrated through a real data set.

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File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(04)00213-1
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Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 96 (2005)
Issue (Month): 2 (October)
Pages: 311-331

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Handle: RePEc:eee:jmvana:v:96:y:2005:i:2:p:311-331
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  1. Léopold Simar & Paul Wilson, 2000. "Statistical Inference in Nonparametric Frontier Models: The State of the Art," Journal of Productivity Analysis, Springer, vol. 13(1), pages 49-78, January.
  2. Léopold Simar, 2003. "Detecting Outliers in Frontier Models: A Simple Approach," Journal of Productivity Analysis, Springer, vol. 20(3), pages 391-424, November.
  3. 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.
  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.
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