A shrinkage approach to joint estimation of multiple covariance matrices

Zongliang Hu, Zhishui Hu, Kai Dong, Tiejun Tong*, Yuedong Wang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)339-374
Number of pages36
Issue number3
Early online date19 Jun 2020
Publication statusPublished - Apr 2021

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Covariance matrices
  • Joint estimation
  • Optimal estimator
  • Quadratic loss function
  • Shrinkage parameter
  • Stein loss function


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