A shrinkage approach to joint estimation of multiple covariance matrices

Zongliang Hu, Zhishui Hu, Kai Dong, Tiejun Tong () and Yuedong Wang
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Zongliang Hu: Shenzhen University
Zhishui Hu: University of Science and Technology of China
Kai Dong: Hong Kong Baptist University
Tiejun Tong: Hong Kong Baptist University
Yuedong Wang: University of California

Metrika: International Journal for Theoretical and Applied Statistics, 2021, vol. 84, issue 3, No 3, 339-374

Abstract: Abstract 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.

Keywords: Covariance matrices; Joint estimation; Optimal estimator; Quadratic loss function; Shrinkage parameter; Stein loss function (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00184-020-00781-3

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