scholarly journals High-dimensional covariance matrix estimation with missing observations

Bernoulli ◽  
2014 ◽  
Vol 20 (3) ◽  
pp. 1029-1058 ◽  
Author(s):  
Karim Lounici
Keyword(s):  
Covariance Matrix ◽  
Covariance Matrix Estimation ◽  
High Dimensional ◽  
Missing Observations ◽  
Matrix Estimation

scholarly journals A Comparison of Methods for Estimating the Determinant of High-Dimensional Covariance Matrix

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Zongliang Hu ◽  
Kai Dong ◽  
Wenlin Dai ◽  
Tiejun Tong
Keyword(s):  
Covariance Matrix ◽  
Statistical Tests ◽  
Estimation Methods ◽  
Covariance Matrix Estimation ◽  
High Dimensional ◽  
Simulation Studies ◽  
Data Set ◽  
Matrix Estimation ◽  
Comparison Results ◽  
Practical Guidelines

Abstract The determinant of the covariance matrix for high-dimensional data plays an important role in statistical inference and decision. It has many real applications including statistical tests and information theory. Due to the statistical and computational challenges with high dimensionality, little work has been proposed in the literature for estimating the determinant of high-dimensional covariance matrix. In this paper, we estimate the determinant of the covariance matrix using some recent proposals for estimating high-dimensional covariance matrix. Specifically, we consider a total of eight covariance matrix estimation methods for comparison. Through extensive simulation studies, we explore and summarize some interesting comparison results among all compared methods. We also provide practical guidelines based on the sample size, the dimension, and the correlation of the data set for estimating the determinant of high-dimensional covariance matrix. Finally, from a perspective of the loss function, the comparison study in this paper may also serve as a proxy to assess the performance of the covariance matrix estimation.

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