Lower bounds on the rate of convergence of nonparametric regression estimates

被引：10

作者：

Antos, A

Györfi, L

Kohler, M

机构：

[1] Tech Univ Budapest, Dept Comp Sci & Informat Theory, H-1521 Budapest, Hungary

[2] Univ Stuttgart, Inst Math A, D-70569 Stuttgart, Germany

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 2000年 / 83卷 / 01期

关键词：

individual rates of convergence; nonparametric regression;

D O I：

10.1016/S0378-3758(99)00084-1

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 show that there exist individual lower bounds on the rare of convergence of nonparametric regression estimates, which are arbitrarily close to Stone's minimax lower bounds, (C) 2000 Elsevier Science B.V. All rights reserved. MSC: primary 62G20; secondary 62G05.

引用

收藏

页码：91 / 100

页数：10

相关论文

共 14 条

[1] Strong minimax lower bounds for learning [J].

Antos, A ;

Lugosi, G .

MACHINE LEARNING, 1998, 30 (01) :31-56

[2]

BARRON A, 1995, 9554 U PAR SUD

[3] ON ESTIMATING A DENSITY USING HELLINGER DISTANCE AND SOME OTHER STRANGE FACTS [J].

BIRGE, L .

PROBABILITY THEORY AND RELATED FIELDS, 1986, 71 (02) :271-291

[4] DISTRIBUTION-FREE LOWER BOUNDS IN DENSITY-ESTIMATION [J].

DEVROYE, L ;

PENROD, CS .

ANNALS OF STATISTICS, 1984, 12 (04) :1250-1262

[5] ON THE STRONG UNIVERSAL CONSISTENCY OF NEAREST-NEIGHBOR REGRESSION FUNCTION ESTIMATES [J].

DEVROYE, L ;

GYORFI, L ;

KRZYZAK, A ;

LUGOSI, G .

ANNALS OF STATISTICS, 1994, 22 (03) :1371-1385

[6] ANY DISCRIMINATION RULE CAN HAVE AN ARBITRARILY BAD PROBABILITY OF ERROR FOR FINITE-SAMPLE SIZE [J].

DEVROYE, L .

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 1982, 4 (02) :154-157

[7]

Devroye L., 1996, A probabilistic theory of pattern recognition

[8] DISTRIBUTION-FREE CONSISTENCY RESULTS IN NONPARAMETRIC DISCRIMINATION AND REGRESSION FUNCTION ESTIMATION [J].

DEVROYE, LP ;

WAGNER, TJ .

ANNALS OF STATISTICS, 1980, 8 (02) :231-239

[9]

IBRAGIMOV IA, 1980, DOKL AKAD NAUK SSSR+, V252, P780

[10]

Ibragimov IA, 1981, STAT ESTIMATION ASYM