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L 1-optimal linear programming estimator for periodic frontier functions with Hölder continuous derivative

  • System Analysis and Operations Research
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Abstract

We propose a new estimator based on a linear programming method for smooth frontiers of sample points on a plane. The derivative of the frontier function is supposed to be Hölder continuous. The estimator is defined as a linear combination of kernel functions being sufficiently regular, covering all the points and whose associated support is of smallest surface. The coefficients of the linear combination are computed by solving a linear programming problem. The L 1 error between the estimated and the true frontier function is shown to be almost surely converging to zero, and the rate of convergence is proved to be optimal.

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Authors and Affiliations

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

    A. V. Nazin

  2. LJK, Inria Rhône-Alpes, Grenoble, France

    S. Girard

Authors
  1. A. V. Nazin
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  2. S. Girard
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Correspondence to A. V. Nazin.

Additional information

Original Russian Text © A.V. Nazin, S. Girard, 2014, published in Avtomatika i Telemekhanika, 2014, No. 12, pp. 78–100.

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Nazin, A.V., Girard, S. L 1-optimal linear programming estimator for periodic frontier functions with Hölder continuous derivative. Autom Remote Control 75, 2152–2169 (2014). https://doi.org/10.1134/S0005117914120066

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  • DOI: https://doi.org/10.1134/S0005117914120066

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