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Sub-Gaussian Estimation of the Scatter Matrix in Ultra-High Dimensional Elliptical Factor Models with 2 + eth Moment

Author

Listed:
  • Yi Ding

    (Faculty of Business Administration, University of Macau)

  • Xinghua Zheng

    (Department of ISOM, Hong Kong University of Science and Technology)

Abstract

We study the estimation of scatter matrices in elliptical factor models with 2 + eth moment. For such heavy-tailed data, robust estimators like the Hubertype estimator in Fan et al. (2018) cannot achieve a sub-Gaussian convergence rate. In this paper, we develop an idiosyncratic-projected self-normalization method to remove the effect of the heavy-tailed scalar component and propose a robust estimator of the scatter matrix that achieves the sub-Gaussian rate under an ultra-high dimensional setting. Such a high convergence rate leads to superior performance in estimating high-dimensional global minimum variance portfolios.

Suggested Citation

  • Yi Ding & Xinghua Zheng, 2025. "Sub-Gaussian Estimation of the Scatter Matrix in Ultra-High Dimensional Elliptical Factor Models with 2 + eth Moment," Working Papers 202529, University of Macau, Faculty of Business Administration.
    • Handle: RePEc:boa:wpaper:202529
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    References listed on IDEAS

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    Keywords

    High-dimension; elliptical model; factor model; scatter matrix; robust estimation;
    All these keywords.

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