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<p>High-dimensional compositional data arises in many research areas. The key question in compositional data analysis is to infer its covariance structure. This paper firstly proposes pilot estimator to estimate the sparse covariance structure of compositional data, and three examples of pilot estimator are provided under bounded fourth moment condition. Then the upper error bounds of the adaptive thresholding pilot estimator are measured by spectral and Frobenius norms. Moreover, we establish the support recovery property of thresholding pilot estimator. Finally, numerical experiments demonstrate the validity of the proposed method.</p>

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Robust sparse covariance matrix estimation for high-dimensional compositional data under lower moment assumption

  • 期刊论文

  • 发表日期：

    2025年8月21日

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  • Huimin Li

摘要

High-dimensional compositional data arises in many research areas. The key question in compositional data analysis is to infer its covariance structure. This paper firstly proposes pilot estimator to estimate the sparse covariance structure of compositional data, and three examples of pilot estimator are provided under bounded fourth moment condition. Then the upper error bounds of the adaptive thresholding pilot estimator are measured by spectral and Frobenius norms. Moreover, we establish the support recovery property of thresholding pilot estimator. Finally, numerical experiments demonstrate the validity of the proposed method.