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

Hu Zongliang (), Dong Kai (), Dai Wenlin () and Tong Tiejun ()
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Hu Zongliang: Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
Dong Kai: Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
Dai Wenlin: CEMSE Division, King Abdullah University of Science and Technology, Jeddah, Saudi Arabia
Tong Tiejun: Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

The International Journal of Biostatistics, 2017, vol. 13, issue 2, 24

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.

Keywords: covariance matrix; high-dimensional data; log-determinant; sparse matrix; shrinkage estimation; thresholding estimation (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1515/ijb-2017-0013

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