STEIN ESTIMATION FOR THE DRIFT OF GAUSSIAN PROCESSES USING THE MALLIAVIN CALCULUS

被引：21

作者：

Privault, Nicolas ^{[1
]}

Reveillac, Anthony ^{[2
]}

机构：

[1] City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China

[2] Univ La Rochelle, Math Lab, F-17042 La Rochelle, France

来源：

ANNALS OF STATISTICS | 2008年 / 36卷 / 05期

关键词：

Nonparametric drift estimation; Stein estimation; Gaussian space; Malliavin calculus; harmonic analysis;

D O I：

10.1214/07-AOS540

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 consider the nonparametric functional estimation of the drift of a Gaussian process via minimax and Bayes estimators. In this context, we construct superefficient estimators of Stein type for such drifts using the Malliavin integration by parts formula and superharmonic functionals on Gaussian space. Our results are illustrated by numerical simulations and extend the construction of James-Stein type estimators for Gaussian processes by Berger and Wolpert [J. Multivariate Anal. 13 (1983) 401-424].

引用

页码：2531 / 2550

页数：20

共 11 条

[1] Stochastic calculus with respect to Gaussian processes [J].

Alòs, E ;

Mazet, O ;

Nualart, D .

ANNALS OF PROBABILITY, 2001, 29 (02) :766-801

[2] ESTIMATING THE MEAN FUNCTION OF A GAUSSIAN PROCESS AND THE STEIN EFFECT [J].

BERGER, J ;

WOLPERT, R .

JOURNAL OF MULTIVARIATE ANALYSIS, 1983, 13 (03) :401-424

[3]

Fourdrinier D, 1998, ANN STAT, V26, P660

[4]

Ibragimov I.A., 1978, Gaussian Random Processes. Applications of Mathematics

[5]

James W., 1961, Berkeley Symposium on Mathematical Statistics and Probability, V1, P361

[6]

Liptser RS, 2001, STAT RANDOM PROCESSE, VII

[7]

Nualart D., 2006, The Malliavin Calculus and Related Topics, Vsecond

[8]

Prakasa Rao BLS, 1999, STAT INFERENCE DIFFU

[9]

R?veillac, 2008, ARXIV08052002V1

[10] ESTIMATION OF THE MEAN OF A MULTIVARIATE NORMAL-DISTRIBUTION [J].

STEIN, CM .

ANNALS OF STATISTICS, 1981, 9 (06) :1135-1151

← 1 2 →