Upper bounds of spiked covariance matrices under differentially private constrains

Chunguang Ren and Pei Zhang

Statistics & Probability Letters, 2025, vol. 226, issue C

Abstract: Cai, Xia, and Zha (2024) presented upper bounds of spiked covariance matrices for Gaussian and sub-Gaussian distributions under the Schatten-q norm, which is a particular type of unitarily invariant norm. In this paper, we also focus on the errors between the true spiked covariance matrices and the covariance matrices with differential privacy under any unitarily invariant norm. Beyond Gaussian and sub-Gaussian populations, we also establish the upper bound of the bounded sub-Gaussian distribution, which is a supplement to the Gaussian and sub-Gaussian cases provided by Cai, Xia, and Zha. It turns out that our estimations are better in some sense.

Keywords: Spiked covariance matrices; Differentially private; Gaussian and sub-Gaussian population; Bounded vectors (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2025.110493

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