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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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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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