Optimal adaptive estimation of a quadratic functional

被引：31

作者：

Cai, T. Tony ^{[1
]}

Low, Mark G. ^{[1
]}

机构：

[1] Univ Penn, Dept Stat, Wharton Sch, Philadelphia, PA 19104 USA

来源：

ANNALS OF STATISTICS | 2006年 / 34卷 / 05期

关键词：

adaptation; block thresholding; quadratic functionals; wavelets; white noise model;

D O I：

10.1214/009053606000000849

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：

Adaptive estimation of a quadratic functional over both Besov and L(p) balls is considered. A collection of nonquadratic estimators are developed which have useful bias and variance properties over individual Besov and L(p) balls. An adaptive procedure is then constructed based on penalized maximization over this collection of nonquadratic estimators. This procedure is shown to be optimally rate adaptive over the entire range of Besov and L(p) balls in the sense that it attains certain constrained risk bounds.

引用

页码：2298 / 2325

页数：28

共 30 条

[1] Model selection for regression on a fixed design [J].

Baraud, Y .

PROBABILITY THEORY AND RELATED FIELDS, 2000, 117 (04) :467-493

[2]

Baraud Y, 2002, BERNOULLI, V8, P577

[3] Risk bounds for model selection via penalization [J].

Barron, A ;

Birgé, L ;

Massart, P .

PROBABILITY THEORY AND RELATED FIELDS, 1999, 113 (03) :301-413

[4]

Bickel P. J., 1993, Efficient and Adaptive Estimation for Semiparametric Models

[5]

BICKEL PJ, 1988, SANKHYA SER A, V50, P381

[6]

BIRGE L., 1997, FESTSCHRIFT L LECAM, P55

[7]

Brown L. D., 1986, FUNDAMENTALS STAT EX

[8]

CAI T, 2006, IN PRESS BERNOULLI

[9] Nonquadratic estimators of a quadratic functional [J].

Cai, TT ;

Low, MG .

ANNALS OF STATISTICS, 2005, 33 (06) :2930-2956

[10] On adaptive estimation of linear functionals [J].

Cai, TT ;

Low, MG .

ANNALS OF STATISTICS, 2005, 33 (05) :2311-2343

← 1 2 3 →