$L_1$-optimal nonparametric frontier estimation via linear programming

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