A shrinkage approach to joint estimation of multiple covariance matrices

In this paper, we propose a shrinkage framework for jointly estimating multiple covariance matrices by shrinking the sample covariance matrices towards the pooled sample covariance matrix. This framework allows us to borrow information across different groups. We derive the optimal shrinkage parameters under the Stein and quadratic loss functions, and prove that our derived estimators are asymptotically optimal when the sample size or the number of groups tends to infinity. Simulation studies demonstrate that our proposed shrinkage method performs favorably compared to the existing methods.