CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST 2012, 28(6) 583-600 DOI:      ISSN: 1001-4268 CN: 31-1256

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The Superiorities of Simultaneous Empirical Bayes Estimation for the Regression Coefficients and Error-Variance in Linear Model

Chen Ling,Wei Laisheng

Department of Statistics and Finance, University of Science & Technology of China, School of Mathematical Science, Anhui University

Abstract��

When the hyperparameters of prior
distribution are partly known in linear model, the simultaneous
parametric empirical Bayes estimators (PEBE) of the regression
coefficients and error variance are constructed. The superiority of
PEBE over the least squares estimator (LSE) of regression
coefficients is investigated in terms of the the mean square error
matrix (MSEM) criterion, and the superiority of PEBE over LSE of the
error variance is discussed under the the mean square error (MSE)
criterion. Finally, when all hyperparameters are unknown, the PEBE
of regression coefficients and error variance are reconstructed and
the superiority of them over LSE under the MSE criterion are studied
by simulation methods.

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