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Avtomat. i Telemekh., 2014, Issue 12, Pages 78–100 (Mi at14164)  

This article is cited in 1 scientific paper (total in 1 paper)

System Analysis and Operations Research

$L_1$-optimal linear programming estimator for periodic frontier functions with Hölder continuous derivative

A. V. Nazina, S. Girardb

a Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia
b LJK, Inria Rhône-Alpes, Grenoble, France

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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English version:
Automation and Remote Control, 2014, 75:12, 2152–2169

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Presented by the member of Editorial Board: . . 

Received: 03.07.2014

Citation: A. V. Nazin, S. Girard, “$L_1$-optimal linear programming estimator for periodic frontier functions with Hölder continuous derivative”, Avtomat. i Telemekh., 2014, no. 12, 78–100; Autom. Remote Control, 75:12 (2014), 2152–2169

Citation in format AMSBIB
\Bibitem{NazGir14}
\by A.~V.~Nazin, S.~Girard
\paper $L_1$-optimal linear programming estimator for periodic frontier functions with H\"older continuous derivative
\jour Avtomat. i Telemekh.
\yr 2014
\issue 12
\pages 78--100
\mathnet{http://mi.mathnet.ru/at14164}
\transl
\jour Autom. Remote Control
\yr 2014
\vol 75
\issue 12
\pages 2152--2169
\crossref{https://doi.org/10.1134/S0005117914120066}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84919359547}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. J. El Methni, L. G. Des, S. Girard, “Kernel estimation of extreme regression risk measures”, Electron. J. Stat., 12:1 (2018), 359–398  crossref  mathscinet  zmath  isi  scopus
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