Robust Empirical Bayes Estimation of the Elliptically Countoured Covariance Matrix
Let S be the matrix of residual sum of square in linear model Y = Aβ + e, where the matrix of errors is distributed as elliptically contoured with unknown scale matrix Σ. For Stein loss function, L1(Σˆ , Σ) = tr(ΣΣˆ −1 )−log |ΣΣˆ −1 |−p, and squared loss function, L2(Σˆ , Σ) = tr(ΣΣˆ −1 −I) 2...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Islamic Azad University
2011-06-01
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| Series: | Journal of Mathematical Extension |
| Online Access: | http://ijmex.com/index.php/ijmex/article/view/76 |
| Summary: | Let S be the matrix of residual sum of square in linear
model Y = Aβ + e, where the matrix of errors is distributed
as elliptically contoured with unknown scale matrix Σ. For Stein
loss function, L1(Σˆ , Σ) = tr(ΣΣˆ −1
)−log |ΣΣˆ −1
|−p, and squared
loss function, L2(Σˆ , Σ) = tr(ΣΣˆ −1 −I)
2
, we offer empirical Bayes
estimators of Σ, which dominate any scalar multiple of S, i.e., aS,
by an effective amount. In fact, this study somehow shows that
improvement of the empirical Bayes estimators obtained under the
normality assumption remains robust under elliptically contoured
model |
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| ISSN: | 1735-8299 1735-8299 |