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

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.

Citation
Hu Z, Dong K, Dai W, Tong T (2017) A Comparison of Methods for Estimating the Determinant of High-Dimensional Covariance Matrix. The International Journal of Biostatistics 13. Available: http://dx.doi.org/10.1515/ijb-2017-0013.

Acknowledgements
Supported by the National Natural Science Foundation of China grant (No. 11671338), and the Hong Kong Baptist University grants FRG2/15-16/019, FRG2/15-16/038 and FRG1/16-17/018.

Publisher
Walter de Gruyter GmbH

Journal
The International Journal of Biostatistics

DOI
10.1515/ijb-2017-0013

Additional Links
https://www.degruyter.com/view/j/ijb.2017.13.issue-2/ijb-2017-0013/ijb-2017-0013.xml

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