Minimax invariant estimation of a continuous distribution function under entropy loss

被引：5

作者：

Mohammadi, L ^{[1
]}

van Zwet, WR ^{[1
]}

机构：

[1] Leiden Univ, Math Inst, NL-2300 RA Leiden, Netherlands

来源：

METRIKA | 2002年 / 56卷 / 01期

关键词：

Entropy; Distribution Function; Loss Function; Decision Problem; Continuous Distribution;

D O I：

10.1007/s001840100152

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：

For the invariant decision problem of estimating a continuous distribution function F with two entropy loss functions, it is proved that the best invariant estimators do exist and are the same as the best invariant estimator of a continuous distribution function under the squared error loss function L(F, d) = integral \F(t) - d(t)\(2) dF(t). They are minimax for any sample size n greater than or equal to 1.

引用

页码：31 / 42

页数：12

共 50 条

[1] Minimax invariant estimation of a continuous distribution function under entropy loss
Leila Mohammadi
Willem R. van Zwet
[J]. Metrika, 2002, 56 : 31 - 42
[2] Minimax invariant estimator of a continuous distribution function under a general loss function
Stepien-Baran, Agnieszka
[J]. METRIKA, 2010, 72 (01) : 37 - 49
[3] Minimax Invariant Estimator of Continuous Distribution Function Under Linex Loss
Jianhui Ning
Minyu Xie
[J]. Journal of Systems Science and Complexity, 2007, 20 : 119 - 126
[4] Minimax invariant estimator of a continuous distribution function under a general loss function
Agnieszka Stępień-Baran
[J]. Metrika, 2010, 72 : 37 - 49
[5] Minimax invariant estimator of continuous distribution function under linex loss
Ning, Jianhui
Xie, Minyu
[J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY, 2007, 20 (01) : 119 - 126
[6] MINIMAX INVARIANT ESTIMATOR OF A CONTINUOUS DISTRIBUTION FUNCTION
YU, QQ
[J]. ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 1992, 44 (04) : 729 - 735
[7] IMPROVED MINIMAX ESTIMATION OF POWERS OF THE VARIANCE OF A MULTIVARIATE NORMAL-DISTRIBUTION UNDER THE ENTROPY LOSS FUNCTION
PAL, N
LING, CH
[J]. STATISTICS & PROBABILITY LETTERS, 1995, 24 (03) : 205 - 211
[8] METHODOLOGY FOR THE INVARIANT ESTIMATION OF A CONTINUOUS DISTRIBUTION FUNCTION
YU, QQ
[J]. ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 1989, 41 (03) : 503 - 520
[9] BEST INVARIANT ESTIMATION OF A DISTRIBUTION FUNCTION UNDER THE KOLMOGOROV-SMIRNOV LOSS FUNCTION
FRIEDMAN, Y
GELMAN, A
PHADIA, E
[J]. ANNALS OF STATISTICS, 1988, 16 (03): : 1254 - 1261
[10] Admissible and Minimax Estimators of a Lower Bounded Scale Parameter of a Gamma Distribution under the Entropy Loss Function
Esfahani, M. Nasr
Nematollahi, N.
[J]. JOURNAL OF MATHEMATICAL EXTENSION, 2009, 4 (01) : 91 - 103

← 1 2 3 4 5 →