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Avtomatika i Telemekhanika, 2005, Issue 12, Pages 143–161 (Mi at1482)  
This article is cited in 7 scientific papers (total in 7 papers)

Stochastic Systems

$L_1$-optimal nonparametric frontier estimation via linear programming

S. Girarda, A. B. Yuditskiia, A. V. Nazinb

a University Grenoble-I, Grenoble, France
b Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia
Full-text PDF (328 kB) Citations (7)
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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 $\beta$-Hölder boundary functions under $\beta\in(0,1]$. 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.
Presented by the member of Editorial Board: B. T. Polyak

Received: 13.01.2005
English version:
Automation and Remote Control, 2005, Volume 66, Issue 12, Pages 2000–2018
DOI: https://doi.org/10.1007/s10513-005-0231-x
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. Girard, A. B. Yuditskii, A. V. Nazin, “$L_1$-optimal nonparametric frontier estimation via linear programming”, Avtomat. i Telemekh., 2005, no. 12, 143–161; Autom. Remote Control, 66:12 (2005), 2000–2018
Citation in format AMSBIB
\Bibitem{GirYudNaz05}
\by S.~Girard, A.~B.~Yuditskii, A.~V.~Nazin
\paper $L_1$-optimal nonparametric frontier estimation via linear programming
\jour Avtomat. i Telemekh.
\yr 2005
\issue 12
\pages 143--161
\mathnet{http://mi.mathnet.ru/at1482}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2196469}
\zmath{https://zbmath.org/?q=an:1267.62048}
\transl
\jour Autom. Remote Control
\yr 2005
\vol 66
\issue 12
\pages 2000--2018
\crossref{https://doi.org/10.1007/s10513-005-0231-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-29144467869}
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  • https://www.mathnet.ru/eng/at/y2005/i12/p143
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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