OPTIMAL AND ROBUST KERNEL ALGORITHMS FOR PASSIVE STOCHASTIC-APPROXIMATION

被引：4

作者：

NAZIN, AV ^{[1
]}

POLYAK, BT ^{[1
]}

TSYBAKOV, AB ^{[1
]}

机构：

[1] ACAD SO RUSSIA,INST PROBLEMS INFORMAT TRANSMISS,MOSCOW 101447,USSR

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 1992年 / 38卷 / 05期

关键词：

PASSIVE STOCHASTIC APPROXIMATION; ROBUST ESTIMATION;

D O I：

10.1109/18.149511

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The problem of estimating a root of an equation, f(x) = 0, is considered in the situation where the values of f(x) are measured with random errors at random points and the choice of these points cannot be controlled. Nonlinear modification of the recursive Hardle-Nixdorf method is studied. Almost sure and mean square convergence is proved, the rate of convergence is estimated. Optimal choice of parameters and of a kernel is presented; it is shown that for the optimal procedure the lower bound for the accuracy of arbitrary methods of solving the problem is attained.

引用

页码：1577 / 1583

页数：7

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