Robust nonparametric estimators of monotone boundaries
(2005) Journal of Multivariate Analysis — Vol. 96, n° 2, p. 311-331 (2005)
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- Abstract
- This paper revisits some asymptotic properties of the robust nonparametric estimators of order-in and order-alpha quantile frontiers and proposes isotonized version of these estimators. Previous convergence properties of the order-in frontier are extended (from weak uniform convergence to complete uniform convergence). Complete uniform convergence of the order-in (and of the quantile order-alpha) nonparametric estimators to the boundary is also established, for an appropriate choice of in (and of a, respectively) as a function of the sample size. The new isotonized estimators share the asymptotic Aa 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. (c) 2004 Elsevier Inc. All rights reserved.
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Daouia, A., & Simar, L. (2005). Robust nonparametric estimators of monotone boundaries. Journal of Multivariate Analysis, 96(2), 311-331. https://doi.org/10.1016/j.jmva.2004.10.005 (Original work published 2005)