Soft thresholding wavelet shrinkage estimation for mean matrix of matrix-variate normal distribution: low and high dimensional.

One of the most important issues in matrix-variate normal distribution is the mean matrix parameter estimation problem. In this paper, we introduce a new soft-threshold wavelet shrinkage estimator based on Stein's unbiased risk estimate (SURE) for the matrix-variate normal distribution. We focus on particular thresholding rules to obtain a new SURE threshold and we produce new estimators under balanced loss function. In addition, we obtain the restricted soft-threshold wavelet shrinkage estimator based on non-negative sub matrix of the mean matrix. Also, we obtain the soft-threshold wavelet shrinkage estimator in high dimensional cases. Denoising real data set is one of the challenges in this field. In this regard, we present a simulation study to test the validity of proposed estimator and provide real examples in low and high-dimensional case. After denoising the real data sets, by computing average mean square error, we find that the new estimator dominates other competing estimators. [ABSTRACT FROM AUTHOR]