Robust Empirical Bayes Estimation of the Elliptically Countoured Covariance Matrix

Authors

  • Zahra Khodadadi
  • Bahram Tarami

DOI:

https://doi.org/10.30495/jme.v0i0.76

Keywords:

Covariance matrix, elliptically contoured, empirical Bayes estimators

Abstract

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(ΣˆΣ−1)−log|ΣˆΣ−1|−p, and squared loss function, L2 (Σˆ , Σ) = tr(Σˆ Σ−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.

Author Biographies

Zahra Khodadadi

Department of Mathematics Assistant Professor of Mathematics Islamic Azad University-Marvdasht Branch Marvdasht, Iran.

Bahram Tarami

Department of Mathematics Assistant Professor of Mathematics College of Sciences, Yasouj University Yasouj, Iran

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Published

2011-05-01

Issue

Vol 5 (2010-2011)

Section

Vol. 5, No. 2(1), (2011)

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