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Automation and Remote Control

, Volume 75, Issue 12, pp 2152–2169 | Cite as

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

  • A. V. Nazin
  • S. Girard
System Analysis and Operations Research
  • 39 Downloads

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.

Keywords

Kernel Function Remote Control Lipschitz Constant Kernel Regression Planning Inference 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Trapeznikov Institute of Control SciencesRussian Academy of SciencesMoscowRussia
  2. 2.LJKInria Rhône-AlpesGrenobleFrance

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