Remarks on extremal problems in nonparametric curve estimation

被引：10

作者：

Leonov, SL ^{[1
]}

机构：

[1] Univ So Calif, Ctr Appl Math Sci, Los Angeles, CA 90089 USA

来源：

STATISTICS & PROBABILITY LETTERS | 1999年 / 43卷 / 02期

关键词：

minimax risk; exact constants; Holder function class; optimal recovery;

D O I：

10.1016/S0167-7152(98)00256-9

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 discuss optimization problems which arise in various nonparametric statistical settings with Holder function classes. We establish a new property of the solution of an optimal recovery problem which leads to exact constants in the formulas for asymptotic minimax risks. (C) 1999 Elsevier Science B.V. All rights reserved.

引用

页码：169 / 178

页数：10

共 22 条

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

DONOHO, DL ;

LOW, MG .

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

[2] ASYMPTOTIC MINIMAX RISK FOR SUP-NORM LOSS - SOLUTION VIA OPTIMAL RECOVERY [J].

DONOHO, DL .

PROBABILITY THEORY AND RELATED FIELDS, 1994, 99 (02) :145-170

[3] NON-PARAMETRIC ESTIMATION OF A MULTIVARIATE PROBABILITY DENSITY [J].

EPANECHN.VA .

THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1969, 14 (01) :153-&

[4]

FULLER AT, 1960, P 1 INT IFAC C MOSC, V2, P584

[5]

GASSER T, 1985, J ROY STAT SOC B MET, V47, P238

[6]

Gasser T., 1979, LECT NOTES MATH, P23, DOI DOI 10.1007/BFB0098489

[7]

Hardle W., 1990, Applied Nonparametric Regression

[8]

Hasminskii R.Z., 1981, STAT ESTIMATION ASYM

[9]

Korostelev A, 1996, ANN STAT, V24, P1075

[10]

KOROSTELEV AP, 1995, 153 WEIE I APPL AN S

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