Nonparametric Frontier Estimation by Linear Programming

Abstract : A new method for estimating the frontier of a set of points (or a support, in other words) is proposed. The estimates are defined as kernel functions covering all the points and whose associated support is of smallest surface. They are written as linear combinations of kernel functions applied to the points of the sample. The weights of the linear combination are then computed by solving a linear programming problem. In the general case, the solution of the optimization problem is sparse, that is, only a few coefficients are non zero. The corresponding points play the role of support vectors in the statistical learning theory. The L 1-norm for the error of estimation is shown to be almost surely converging to zero, and the rate of convergence is provided.
Keywords : LEAR
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Article dans une revue
Automation and Remote Control / Avtomatika i Telemekhanika, MAIK Nauka/Interperiodica, 2004, 65 (1), pp.58--64. 〈http://www.springerlink.com/content/w847544566237g14/〉. 〈10.1023/B:AURC.0000011690.13220.58〉
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Soumis le : lundi 20 décembre 2010 - 08:42:16
Dernière modification le : jeudi 28 juin 2018 - 14:38:10

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Guillaume Bouchard, Stephane Girard, Anatoli Iouditski, Alexander Nazin. Nonparametric Frontier Estimation by Linear Programming. Automation and Remote Control / Avtomatika i Telemekhanika, MAIK Nauka/Interperiodica, 2004, 65 (1), pp.58--64. 〈http://www.springerlink.com/content/w847544566237g14/〉. 〈10.1023/B:AURC.0000011690.13220.58〉. 〈inria-00548244〉

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