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
收藏
页码：330 / 339
页数：10
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