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L 1-Optimal Nonparametric Frontier Estimation via Linear Programming

  • Stochastic Systems
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Abstract

A frontier estimation method for a set of points on a plane is proposed, being optimal in L 1-norm on a given class of β-Holder boundary functions under β ∈ (0, 1]. The estimator is defined as sufficiently regular linear combination of kernel functions centered in the sample points, which covers all these points and whose associated support is of minimal surface. The linear combination weights are calculated via solution of the related linear programming problem. The L 1-norm of the estimation error is demonstrated to be convergent to zero with probability one, with the optimal rate of convergence.

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Authors and Affiliations

  1. LMC-IMAG, University Grenoble-I, Grenoble, France

    S. Girard & A. Iouditski

  2. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    A. V. Nazin

Authors
  1. S. Girard
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  2. A. Iouditski
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  3. A. V. Nazin
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Additional information

__________

Translated from Avtomatika i Telemekhanika, No. 12, 2005, pp. 143–161.

Original Russian Text Copyright © 2005 by Girard, Iouditski, Nazin.

The research has been carried out during the visits to LMC-IMAG (Grenoble-I University) and INRIA Rhone-Alpes, MISTIS project, France, in the year of 2004.

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Girard, S., Iouditski, A. & Nazin, A.V. L 1-Optimal Nonparametric Frontier Estimation via Linear Programming. Autom Remote Control 66, 2000–2018 (2005). https://doi.org/10.1007/s10513-005-0231-x

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  • DOI: https://doi.org/10.1007/s10513-005-0231-x

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