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Comparison of linear shrinkage estimators of a large covariance matrix in normal and non-normal distributions

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  • Ikeda, Yuki
  • Kubokawa, Tatsuya
  • Srivastava, Muni S.

Abstract

The problem of estimating the large covariance matrix of both normal and non-normal distributions is addressed. In convex combinations of the sample covariance matrix and a positive definite target matrix, the optimal weight is estimated by exact or approximate unbiased estimators of the numerator and denominator of the optimal weight in normal or non-normal cases. A spherical and a diagonal matrices are two typical examples of target matrices, and the corresponding single shrinkage estimators are provided. A double shrinkage estimator which shrinks the sample covariance matrix toward the two target matrices is also suggested. The performances of single and double shrinkage estimators are numerically investigated through simulation and empirical studies.

Suggested Citation

  • Ikeda, Yuki & Kubokawa, Tatsuya & Srivastava, Muni S., 2016. "Comparison of linear shrinkage estimators of a large covariance matrix in normal and non-normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 95-108.
    • Handle: RePEc:eee:csdana:v:95:y:2016:i:c:p:95-108
    DOI: 10.1016/j.csda.2015.09.011
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    2. Besson, Olivier & Vincent, François & Gendre, Xavier, 2020. "A Stein’s approach to covariance matrix estimation using regularization of Cholesky factor and log-Cholesky metric," Statistics & Probability Letters, Elsevier, vol. 167(C).
    3. Benoit Oriol & Alexandre Miot, 2023. "Ledoit-Wolf linear shrinkage with unknown mean," Papers 2304.07045, arXiv.org.

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