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Reports Year : 2005

Linear programming problems for $L_1$ optimal frontier estimation

Anatoli B. Juditsky
Alexander Nazin
  • Function : Author


We propose new optimal estimators for the Lipschitz frontier of a set of points. They are defined as kernel estimators being sufficiently regular, covering all the points and whose associated support is of smallest surface. The estimators are written as linear combinations of kernel functions applied to the points of the sample. The coefficients of the linear combination are then computed by solving related linear programming problem. The $L_1$ error between the estimated and the true frontier function with a known Lipschitz constant is shown to be almost surely converging to zero, and the rate of convergence is proved to be optimal.
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Dates and versions

inria-00070541 , version 1 (19-05-2006)


  • HAL Id : inria-00070541 , version 1


Stéphane Girard, Anatoli B. Juditsky, Alexander Nazin. Linear programming problems for $L_1$ optimal frontier estimation. RR-5466, INRIA. 2005, pp.34. ⟨inria-00070541⟩
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