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L1-optimal linear programming estimator for periodic frontier functions with Hölder continuous derivative

Alexander Nazin 1 Stéphane Girard 2
2 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : We propose a new estimator based on a linear programming method for smooth frontiers of sample points. 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 L1- error between the estimated and the true frontier functions is shown to be almost surely converging to zero, and the rate of convergence is proved to be optimal.
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Alexander Nazin, Stéphane Girard. L1-optimal linear programming estimator for periodic frontier functions with Hölder continuous derivative. Automation and Remote Control / Avtomatika i Telemekhanika, MAIK Nauka/Interperiodica, 2014, 75 (12), pp.2152-2169. ⟨10.1134/S0005117914120066⟩. ⟨hal-01066739⟩

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