AN OPTIMAL PROPERTY OF THE GAUSS-MARKOV ESTIMATOR

被引：5

作者：

ALI, MM ^{[1
]}

PONNAPALLI, R ^{[1
]}

机构：

[1] SUNY COLL TECHNOL UTICA ROME,UTICA,NY

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 1990年 / 32卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

elliptical distribution; Gauss-Markoff estimator; linear estimation; maximum probability estimator;

D O I：

10.1016/0047-259X(90)90079-W

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：

Consider the linear model Y = Xβ + ε, where Y is the response variable of order (n×1), X is an (n×p) matrix of known constants, β is a (p×1) unknown parameter, ε is an (n×1) error variable with E(ε) = 0, and E(εε′) = σ2Λ, where Λ is a known (n×n) positive definite matrix and σ2 is a positive scalar, possibly unknown. Suppose that θ is a linear function of the components of β. It is shown that when ε is assumed to have a distribution belonging to the class of elliptical distributions (i.e., distributions having constant density or equiprobable surfaces on homothetic ellipsoids as in the case of the multivariate normal distributions), the probability of the Gauss-Markoff estimator of θ falling inside any fixed ellipsoid centered at θ is greater than or equal to the probability that any linear unbiased estimator of θ falls inside the same ellipsoid. © 1990.

引用

页码：171 / 176

页数：6

共 6 条

[1] ELLIPTICALLY SYMMETRIC DISTRIBUTIONS - A REVIEW AND BIBLIOGRAPHY [J].