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High dimensional T-type Estimator for robust covariance matrix estimation with applications to elliptical factor models

Author

Listed:
  • Guanpeng Wang

    (Weifang University)

  • Hengjian Cui

    (Capital Normal University)

Abstract

In this paper, a regularized t-type estimator is proposed for high-dimensional scatter matrix estimation, where the number of dimensions p is comparable to, or even larger than the sample size n, and its thresholding form is employed to deal with sparse settings. Then, regularized t-type estimator is extended to high-dimensional elliptic factor models with outliers for robust identification of common factor numbers. Finally, we illustrate that the proposed regularized t-type estimator significantly outperforms the competitors through extensive simulations, even in cases with high-dimensional data. Meanwhile, the t-type estimator can significantly improve the efficiency of Tyler’s M-estimator in Goes et al. (Ann Stat 48(1):86–110, 2020) when the samples follow a possibly heavy-tailed elliptical distribution with a non-central or unknown location parameter.

Suggested Citation

  • Guanpeng Wang & Hengjian Cui, 2025. "High dimensional T-type Estimator for robust covariance matrix estimation with applications to elliptical factor models," Computational Statistics, Springer, vol. 40(2), pages 767-794, February.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:2:d:10.1007_s00180-024-01505-1
    DOI: 10.1007/s00180-024-01505-1
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    References listed on IDEAS

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