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High-Dimensional Covariance Matrix Estimation: Shrinkage Toward a Diagonal Target
Author:
Mr. Sakai Ando
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https://orcid.org/0000-0003-2785-4375
and
Mingmei Xiao
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Series:
IMF Working Papers
Volume/Issue:
Volume 2023: Issue 257
Language:
English
Publication Date:
08 Dec 2023
DOI:
https://doi.org/10.5089/9798400260780.001
ISBN:
9798400260780
ISSN:
1018-5941
Pages:
32
Keywords:
High-Dimension; Covariance Matrix; Shrinkage; Diagonal Target; matrix estimation; shrinkage parameter; novel shrinkage estimator; sample correlation matrix; Estimation techniques
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IMF Working Papers describe research in progress by the author(s) and are published to elicit comments and to encourage debate. The views expressed in IMF Working Papers are those of the author(s) and do not necessarily represent the views of the IMF, its Executive Board, or IMF management.
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This paper proposes a novel shrinkage estimator for high-dimensional covariance matrices by extending the Oracle Approximating Shrinkage (OAS) of Chen et al. (2009) to target the diagonal elements of the sample covariance matrix. We derive the closed-form solution of the shrinkage parameter and show by simulation that, when the diagonal elements of the true covariance matrix exhibit substantial variation, our method reduces the Mean Squared Error, compared with the OAS that targets an average variance. The improvement is larger when the true covariance matrix is sparser. Our method also reduces the Mean Squared Error for the inverse of the covariance matrix.
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Cover IMF Working Papers
IMF Working Papers
ISSN:
1018-5941
Publisher:
International Monetary Fund