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AIMS Mathematics

2023, Volume 8, Issue 9: 21439-21462. doi: 10.3934/math.20231092
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Research article

Pilot estimators for a kind of sparse covariance matrices with incomplete heavy-tailed data

  • Department of Mathematics, Beijing University of Technology, Beijing 100124, China
  • Received: 22 March 2023 Revised: 26 June 2023 Accepted: 28 June 2023 Published: 05 July 2023

  • MSC : 62H12, 62J10

  • This paper investigates generalized pilot estimators of covariance matrix in the presence of missing data. When the random samples have only bounded fourth moment, two kinds of generalized pilot estimators are provided, the generalized Huber estimator and the generalized truncated mean estimator. In addition, we construct thresholding generalized pilot estimator for a kind of sparse covariance matrices and establish the convergence rates in terms of probability under spectral and Frobenius norms respectively. Moreover, the convergence rates in sense of expectation are also given under an extra condition. Finally, simulation studies are conducted to demonstrate the superiority of our method.

    Citation: Huimin Li, Jinru Wang. Pilot estimators for a kind of sparse covariance matrices with incomplete heavy-tailed data[J]. AIMS Mathematics, 2023, 8(9): 21439-21462. doi: 10.3934/math.20231092

    Related Papers:

  • This paper investigates generalized pilot estimators of covariance matrix in the presence of missing data. When the random samples have only bounded fourth moment, two kinds of generalized pilot estimators are provided, the generalized Huber estimator and the generalized truncated mean estimator. In addition, we construct thresholding generalized pilot estimator for a kind of sparse covariance matrices and establish the convergence rates in terms of probability under spectral and Frobenius norms respectively. Moreover, the convergence rates in sense of expectation are also given under an extra condition. Finally, simulation studies are conducted to demonstrate the superiority of our method.


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