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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Hu Zongliang & Dong Kai & Dai Wenlin & Tong Tiejun, 2017. "A Comparison of Methods for Estimating the Determinant of High-Dimensional Covariance Matrix," The International Journal of Biostatistics, De Gruyter, vol. 13(2), pages 1-24, November.
    • Handle: RePEc:bpj:ijbist:v:13:y:2017:i:2:p:24:n:7
    DOI: 10.1515/ijb-2017-0013
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    References listed on IDEAS

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    1. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    2. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    3. Cai, Tony & Liu, Weidong, 2011. "Adaptive Thresholding for Sparse Covariance Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 672-684.
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