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

Zongliang Hu*, Kai Dong, Wenlin Dai, Tiejun TONG

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number20170013
JournalInternational Journal of Biostatistics
Volume13
Issue number2
DOIs
Publication statusPublished - 27 Nov 2017

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • covariance matrix
  • high-dimensional data
  • log-determinant,sparse matrix
  • shrinkage estimation
  • thresholding estimation

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