Wavelet Thresholds for Matrix-Variate Normal Distribution Under The Reflected Normal Loss

The matrix-variate normal distribution is a probability distribution that is a generalization of the multivariate normal distribution to matrix-valued random variables. In this paper, we introduce a wavelet shrinkage estimator based on Stein’s unbiased risk estimate (SURE) threshold for matrix-variate normal distribution. We find a new SURE threshold for soft thresholding wavelet shrinkage estimator under the reflected normal loss function in low dimensional cases. Also, we obtain the restricted wavelet shrinkage estimator based on non-negative sub matrix of the mean matrix. Finally, we present a simulation study to test the validity of the wavelet shrinkage.

Keywords:

Matrix , variate normal distribution , Shrinkage estimtion , SURE threshold , Wavelet shrinkage , Reflected normal loss function