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

共 11 条

[1]

[Anonymous], 1977, SOLUTION ILL POSED P

[2]

[Anonymous], 1968, SER DETECTION ESTIMA

[3] RENORMALIZATION EXPONENTS AND OPTIMAL POINTWISE RATES OF CONVERGENCE [J].

DONOHO, DL ;

LOW, MG .

ANNALS OF STATISTICS, 1992, 20 (02) :944-970

[4]

Engl H.W., 1987, Inverse and ill-posed problems

[5]

GOLUBEV GK, 1996, MATH METHODS STAT, V5, P357

[6]

Lavrentiev M.M., 1967, SOME IMPROPERLY POSE

[7] Statistical inverse estimation in Hilbert scales [J].

Mair, BA ;

Ruymgaart, FH .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1996, 56 (05) :1424-1444

[8]

Pinsker M. S., 1980, Problems of Information Transmission, V16, P120

[9]

SUDAKOV VN, 1964, SOV MATH DOKL, V157, P1094

[10]

SULLIVAN FO, 1996, STAT SCI, V1, P502

← 1 2 →