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

页码：419 / 433

页数：15

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