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https://doi.org/10.1214/09-AOS752

has been cited by the following article:

• TITLE: Optimal Estimation of High-Dimensional Covariance Matrices with Missing and Noisy Data

  AUTHORS: Meiyin Wang, Wanzhou Ye

  KEYWORDS: High-Dimensional Covariance Matrix, Missing Data, Sub-Gaussian Noise, Optimal Estimation

  JOURNAL NAME: Advances in Pure Mathematics, Vol.14 No.4, April 15, 2024

  ABSTRACT: The estimation of covariance matrices is very important in many fields, such as statistics. In real applications, data are frequently influenced by high dimensions and noise. However, most relevant studies are based on complete data. This paper studies the optimal estimation of high-dimensional covariance matrices based on missing and noisy sample under the norm. First, the model with sub-Gaussian additive noise is presented. The generalized sample covariance is then modified to define a hard thresholding estimator , and the minimax upper bound is derived. After that, the minimax lower bound is derived, and it is concluded that the estimator presented in this article is rate-optimal. Finally, numerical simulation analysis is performed. The result shows that for missing samples with sub-Gaussian noise, if the true covariance matrix is sparse, the hard thresholding estimator outperforms the traditional estimate method.