L1-optimal nonparametric frontier estimation via linear programming

被引：5
|
作者：
Girard, S [1 ]
Iouditski, A
Nazin, AV
机构：
[1] Univ Grenoble 1, LMC, IMAG, Grenoble, France
[2] Russian Acad Sci, Trapeznikov Inst Control Sci, Moscow, Russia
来源：
AUTOMATION AND REMOTE CONTROL | 2005年 / 66卷 / 12期
关键词：
D O I：
10.1007/s10513-005-0231-x
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
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-Holder boundary functions under beta is an element of (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.
引用
收藏
页码：2000 / 2018
页数：19
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