Target selection in shrinkage estimation of covariance matrix: A structural similarity approach

Xuanci Wang and Bin Zhang

Statistics & Probability Letters, 2024, vol. 208, issue C

Abstract: The shrinkage estimator of a high-dimensional covariance matrix relies on a preassigned target matrix during data processing. This paper provides an adaptive approach for selecting the optimal Toeplitz target matrix. We discover a sufficient and necessary condition for characterizing the two kinds of target matrices with the Toeplitz structure, and we propose an adaptive selection algorithm by measuring the similarity between the data and the Toeplitz structure. Numerical simulations and an empirical study on monetary funds verify the effectiveness of the selection approach.

Keywords: High-dimensional covariance matrix; Target selection; Linear shrinkage estimation; Toeplitz structure (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110048

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