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<p>Estimating high-dimensional covariance matrices is a cornerstone of modern multivariate statistical analysis. However, current research rarely examines the robustness of high-dimensional covariance estimators to outliers. In this paper, we extend the traditional <i>T</i>-type estimator to high-dimensional settings through a regularization method. Specifically, we construct a convex combination of a positive definite target matrix and the covariance matrix of the current iteration step to address the singularity and ill-conditioning issues. We propose a criterion to determine the weighting coefficient by constraining the condition number of the matrix. We also theoretically prove the convergence of the algorithm. Extensive simulation studies demonstrate that the proposed estimator has a superior rapid convergence property and significantly outperforms competitors in high-dimensional settings. In the analysis of real data, we show that the <i>T</i>-type estimator enhances the performance of discriminant and classification tasks.</p>

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A regularized T-type estimator for high-dimensional data

  • 期刊论文

  • 发表日期：

    2026年1月21日

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  • Rui Zhang,
  • Wan Tian,
  • Bo Zhang,
  • Hengjian Cui

摘要

Estimating high-dimensional covariance matrices is a cornerstone of modern multivariate statistical analysis. However, current research rarely examines the robustness of high-dimensional covariance estimators to outliers. In this paper, we extend the traditional T-type estimator to high-dimensional settings through a regularization method. Specifically, we construct a convex combination of a positive definite target matrix and the covariance matrix of the current iteration step to address the singularity and ill-conditioning issues. We propose a criterion to determine the weighting coefficient by constraining the condition number of the matrix. We also theoretically prove the convergence of the algorithm. Extensive simulation studies demonstrate that the proposed estimator has a superior rapid convergence property and significantly outperforms competitors in high-dimensional settings. In the analysis of real data, we show that the T-type estimator enhances the performance of discriminant and classification tasks.