Frontier estimation with kernel regression on high order moments

Authors:
StéPhane Girard;Armelle Guillou;Gilles Stupfler
Affiliations:
Team Mistis, INRIA Rhône-Alpes & LJK, Inovalléée, 655, av. de l'Europe, Montbonnot, 38334 Saint-Ismier cedex, France;Université de Strasbourg & CNRS, IRMA, UMR 7501, 7 rue Renéé Descartes, 67084 Strasbourg cedex, France;Université d'Aix-Marseille, CERGAM, 15-19 allée Claude Forbin, 13628 Aix-en-Provence Cedex 1, France
Venue:
Journal of Multivariate Analysis
Year:
2013

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Abstract

We present a new method for estimating the frontier of a multidimensional sample. The estimator is based on a kernel regression on high order moments. It is assumed that the order of the moments goes to infinity while the bandwidth of the kernel goes to zero. The consistency of the estimator is proved under mild conditions on these two parameters. The asymptotic normality is also established when the conditional distribution function decreases at a polynomial rate to zero in the neighborhood of the frontier. The good performance of the estimator is illustrated in some finite sample situations.