Mahmoud Afshari

Suppose that the random matrix Xp×m has a matrix variate normal distribution with the mean matrix Θ and covariance matrix Σ ⊗ Ψ where Σ and Ψ are known positive definite covariance matrices. This paper studies the soft bayesian shrinkage wavelet estimation of the mean matrix Θ. Soft bayesian shrinkage wavelet estimator is proposed based on quadratic balanced loss function and matrix variate nor mal Np,m(0, Λ ⊗ Ψ) prior distribution. Λ is known positive definite covariance matrix. By using bayes estimator as the target estimator in quadratic balanced loss function and Stien’s unbiased risk estimate technique, the soft bayesian shrinkage wavelet threshold is obtained. Based on new proposed threshold, we find the soft bayesian shrinkage wavelet estimator of Θ mean matrix. The simulation study and two real examples to measure the performance of the presented theoretical topics are used. The results show that the soft bayesian shrinkage wavelet estimator dominates classical shrinkage wavelet estimators