The risk of tensor Stein-rules in elliptically contoured distributions

Abstract

In this paper, we consider an estimation problem of a tensor parameter of a random tensor which follows elliptically contoured distribution. We establish the risk functions of a class of tensor shrinkage estimators of the mean parameter tensor of a random tensor which follows an elliptically contoured distribution. In particular, we generalize some recent findings in three ways. First, the problem considered extends the one about a matrix estimation. Second, we generalize some recent identities which are useful in establishing the risk of tensor shrinkage estimators. Third, we derive a more general sufficient condition for the tensor shrinkage estimators to dominate the unrestricted estimator. The additional novelty of the derived results consists in the fact that, on the top of the complexity related to tensor random fact, the case considered here takes into account a possible correlation between the shrinking factor and the restricted estimator. Finally, in order to illustrate the applications of the proposed method, we present some simulation results and a real dataset analysis.

Acknowledgements

The authors would like to thank the referees for helpful comments and useful insights. Further, Dr. Nkurunziza would like to acknowledge the financial support received from the Natural Sciences and Engineering Research Council of Canada (NSERC).

Disclosure statement

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

Additional information

Funding

This work was supported by Natural Sciences and Engineering Research Council of Canada (NSERC) [RGPIN-2019-04464].