Wavelet Shrinkage Estimation for Mean Matrix of Matrix-Variate Elliptically Contoured Distributions

Finding the appropriate threshold is one of the most important issues in the wavelet shrinkage method. Especially when the goal is to estimate the mean matrix parameter for matrix-variate elliptically contoured distributions. In this paper, we introduce a new soft thresholding wavelet shrinkage estimator based on Stein’s unbiased risk estimate (SURE) for the class of matrix-variate elliptically contoured distributions. We want to find a class of soft wavelet shrinkage SURE estimators under the balanced loss function by the wavelet shrinkage method. For this purpose, we find a class of the soft thresholding wavelet shrinkage estimators under the balanced loss function by the wavelet shrinkage method. Also, we obtain the restricted soft thresholding wavelet shrinkage estimator based on non-negative sub matrix of the mean matrix parameter. Finally, the performance of the proposed estimator was investigated using a simulation study.