Sub-Gaussian High-Dimensional Covariance Matrix Estimation under Elliptical Factor Model with 2 + {\epsilon}th Moment

Yi Ding; Xinghua Zheng

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arXiv · 2406.18347

Sub-Gaussian High-Dimensional Covariance Matrix Estimation under Elliptical Factor Model with 2 + {\epsilon}th Moment

Yi Ding·Xinghua Zheng

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Abstract

We study the estimation of high-dimensional covariance matrices under elliptical factor models with 2 + {\epsilon}th moment. For such heavy-tailed data, robust estimators like the Huber-type estimator in Fan, Liu and Wang (2018) can not achieve sub-Gaussian convergence rate. In this paper, we develop an idiosyncratic-projected self-normalization (IPSN) method to remove the effect of heavy-tailed scalar parameter, and propose a robust pilot estimator for the scatter matrix that achieves the sub-Gaussian rate. We further develop an estimator of the covariance matrix and show that it achieves a faster convergence rate than the generic POET estimator in Fan, Liu and Wang (2018).

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Yi Ding, Xinghua Zheng. 2024-06-26. Sub-Gaussian High-Dimensional Covariance Matrix Estimation under Elliptical Factor Model with 2 + {\epsilon}th Moment. https://arxiv.org/abs/2406.18347

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