On-line Estimation of Smooth Signals with Partial Observation

被引：0

作者：

Chow, P. ^{[1
]}

Khasminskii, R. ^{[1
,2
]}

机构：

[1] Wayne State Univ, Detroit, MI 48202 USA

[2] RAS, Inst Informat Transmiss Problems, Moscow, Russia

来源：

PROBLEMS OF INFORMATION TRANSMISSION | 2006年 / 42卷 / 04期

关键词：

Gaussian White Noise; Information Transmission; Kernel Approximation; Nonlinear Filter; Standard Wiener Process;

D O I：

10.1134/S0032946006040053

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The paper concerns the estimation of a smooth signal S(t) and its derivatives in the presence of a noise depending on a small parameter epsilon based on a partial observation. A nonlinear Kalman-type filter is proposed to perform on-line estimation. For the signal S in a given class of smooth functions, the convergence rate for the estimation risks, as epsilon -> 0, is obtained. It is proved that such rates are optimal in a minimax sense. In contrast to the complete observation case, the rates are reduced, due to incomplete information.

引用

页码：330 / 339

页数：10

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