Low and high dimensional wavelet thresholds for matrix-variate normal distribution

Abstract

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 balanced loss function in low and high 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 estimator and two real examples for low and high dimensional data sets.

Keywords:

• High dimensional
• Matrix-variate normal distribution
• Shrinkage estimator
• SURE threshold
• Wavelet shrinkage method

Acknowledgments

The authors would like to thank the editors and reviewers for their valuable comments, which greatly improved the readability of this paper. Also, we would like to thank the research committee of Persian Gulf University.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors state that no funding source or sponsor has participated in the realization of this work.