Soft Bayesian Shrinkage Wavelet Threshold Estimation of Mean Matrix of the Matrix Variate Normal Distribution under Quadratic Balanced Loss Function

Document Type : Original Paper

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Department of Statistics, Persian Gulf University, 7516913798, Iran

Abstract

Suppose that the random matrix X 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 normal $N_{p,m}(\mathbf{0}, \mathbf{\Lambda}\otimes \mathbf{\Psi})$ prior distribution. Λ is known positive definite covariance matrix. By using the Bayes estimator as the target estimator in the quadratic balanced loss function and Stien's unbiased risk estimate technique, the soft Bayesian shrinkage wavelet threshold is obtained. Based on the 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.

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History

  • Receive Date: 24 October 2023
  • Revise Date: 09 June 2024
  • Accept Date: 08 September 2024

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