High-Dimensional Covariance Matrix Estimation: Shrinkage Toward a Diagonal Target

December 8, 2023

Preview Citation

Format: Chicago

Sakai Ando, and Mingmei Xiao. High-Dimensional Covariance Matrix Estimation: Shrinkage Toward a Diagonal Target, (USA: International Monetary Fund, 2023) accessed November 21, 2024

Disclaimer: 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.

Summary

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.

Subject: Econometric analysis, Estimation techniques

Keywords: Covariance Matrix, Diagonal Target, Estimation techniques, High-Dimension, Matrix estimation, Novel shrinkage estimator, Sample correlation matrix, Shrinkage, Shrinkage parameter

Publication Details

Pages:

32
Volume:

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DOI:

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Issue:

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Series:

Working Paper No. 2023/257
Stock No:

WPIEA2023257
ISBN:

9798400260780
ISSN:

1018-5941

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