A statistical approach to the cauchy problem for the Laplace equation

被引：8
|
作者：
Golubev, G [1 ]
Khasminskii, R [1 ]
机构：
[1] Univ Aix Marseille 1, Ctr Math & Informat, F-13453 Marseille, France
来源：
STATE OF THE ART IN PROBABILITY AND STATISTICS: FESTSCHRIFT FOR WILLEM R VAN ZWET | 2001年 / 36卷
关键词：
ill-posed problems; statistical approach; asymptotically minimax estimator;
D O I：
10.1214/lnms/1215090081
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We study the problem of estimating an unknown solution of the Cauchy problem for the Laplace equation, with L-2-norm loss, when the initial conditions are observed in a white Gaussian noise with a small spectral density. It is shown in particular that asymptotically minimax estimators are as a rule nonlinear.
引用
收藏
页码：419 / 433
页数：15
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