On the Loss Robustness of Least-Square Estimators

被引：0

作者：

Ghosh, Tamal ^{[1
]}

Ghosh, Malay ^{[1
]}

Kubokawa, Tatsuya ^{[2
]}

机构：

[1] Univ Florida, Dept Stat, 700 SW 16th Ave,209, Gainesville, FL 32601 USA

[2] Univ Tokyo, Grad Sch Econ, Tokyo, Japan

来源：

AMERICAN STATISTICIAN | 2020年 / 74卷 / 01期

关键词：

Divergence; Gauss-Markov theorem; Linear Risk minimization; Unbiased estimators;

D O I：

10.1080/00031305.2018.1529626

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：

The article revisits univariate and multivariate linear regression models. It is shown that least-square estimators (LSEs) are minimum risk estimators in general class of linear unbiased estimators under some general divergence loss. This amounts to the loss robustness of LSEs.

引用

页码：64 / 67

页数：4

共 50 条

[1] A COMPARISON OF BAYES ESTIMATORS AND CONSTRAINED LEAST-SQUARE ESTIMATORS
GRUBER, MHJ
[J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 1985, 14 (02) : 479 - 489
[2] On the statistical properties of least-square estimators of layered neural networks
[J]. Kitahara, M, 1600, John Wiley and Sons Inc. (35):
[3] CONVERGENCE THEOREMS ON LEAST-SQUARE ESTIMATORS OF STRUCTURAL PARAMETERS OF A LINEAR EXPLOSIVE MODEL
VENKATAR.KN
[J]. ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 1974, 26 (01) : 61 - 85
[4] Least-square fitting with spheres
Spath, H
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1998, 96 (01) : 191 - 199
[5] Least-square circles in the plane
Krystek, M
[J]. TECHNISCHES MESSEN, 2004, 71 (05): : 319 - 323
[6] LEAST-SQUARE EXPONENTIAL APPROXIMATION
DIAMESSIS, JE
[J]. ELECTRONICS LETTERS, 1972, 8 (18) : 454 - +
[7] RANDOM LEAST-SQUARE ANALYSIS
DOWDEE, JW
SOONG, TT
[J]. SIAM REVIEW, 1973, 15 (01) : 251 - +
[8] Least-Square Fitting with Spheres
H. Späth
[J]. Journal of Optimization Theory and Applications, 1998, 96 : 191 - 199
[9] RANDOM LEAST-SQUARE ANALYSIS
DOWDEE, JW
SOONG, TT
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1974, 46 (02) : 447 - 462
[10] NEW LEAST-SQUARE ALGORITHMS
DAVIDON, WC
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1976, 18 (02) : 187 - 197

← 1 2 3 4 5 →