Robust nonparametric estimators of monotone boundaries

  • Authors:

  • Abdelaati Daouia;Léopold Simar

  • Affiliations:

  • GREMAQ, Université de Toulouse I and LSP, Université de Toulouse III, France;Institut de Statistique, Université Catholique de Louvain, Voie du Roman Pays 20, B-1348 Louvain-la-Neuve, Belgium

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2005

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Abstract

This paper revisits some asymptotic properties of the robust nonparametric estimators of order-m and order-@a 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-@a) nonparametric estimators to the boundary is also established, for an appropriate choice of m (and of @a, 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.