Frontier estimation with kernel regression on high order moments
Journal of Multivariate Analysis
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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.