Robust Improvement in Estimation of a Covariance Matrix in an Elliptically Contoured Distribution Respect to Quadratic Loss Function
Abstract
Let S be matrix of residual sum of square in linear
model Y = A¯ + e where matrix e is distributed as elliptically
contoured with unknown scale matrix §. In present work, we con-
sider the problem of estimating § with respect to squared loss
function, L(^§;§) = tr( ^§§¡1¡I)2. It is shown that improvement
of the estimators were obtained by James, Stein [7], Dey and Sri-
vasan [1] under the normality assumption remains robust under an
elliptically contoured distribution respect to squared loss function.
model Y = A¯ + e where matrix e is distributed as elliptically
contoured with unknown scale matrix §. In present work, we con-
sider the problem of estimating § with respect to squared loss
function, L(^§;§) = tr( ^§§¡1¡I)2. It is shown that improvement
of the estimators were obtained by James, Stein [7], Dey and Sri-
vasan [1] under the normality assumption remains robust under an
elliptically contoured distribution respect to squared loss function.
Keywords
Covariance matrix, elliptically con-
toured distribution, expected value, multivariate linear model, squared
loss.
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