Robust nonparametric estimators of monotone boundaries

Abdelaati Daouia () and Leopold Simar

Journal of Multivariate Analysis, 2005, vol. 96, issue 2, 311-331

Abstract: 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.

Keywords: Estimation; of; a; monotone; boundary; Robust; nonparametric; estimators; Isotonization; procedure; Complete; uniform; convergence; Exponential; probability; inequalities (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (35)

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