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Non-asymptotic error controlled sparse high dimensional precision matrix estimation

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  • Kashlak, Adam B.

Abstract

Estimation of a high dimensional precision matrix is a critical problem to many areas of statistics including Gaussian graphical models and inference on high dimensional data. Working under the structural assumption of sparsity, we propose a novel methodology for estimating such matrices while controlling the false positive rate, percentage of matrix entries incorrectly chosen to be non-zero. We specifically focus on false positive rates tending towards zero with finite sample guarantees. In the context of large scale hypothesis testing, control of the false discovery rate is also considered. This methodology is distribution free, but is particularly applicable to the problem of Gaussian network recovery. We also consider applications to constructing gene networks in genomics data.

Suggested Citation

  • Kashlak, Adam B., 2021. "Non-asymptotic error controlled sparse high dimensional precision matrix estimation," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:jmvana:v:181:y:2021:i:c:s0047259x20302712
    DOI: 10.1016/j.jmva.2020.104690
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    References listed on IDEAS

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    1. Adam J. Rothman, 2012. "Positive definite estimators of large covariance matrices," Biometrika, Biometrika Trust, vol. 99(3), pages 733-740.
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    4. Jianqing Fan & Yuan Liao & Han Liu, 2016. "An overview of the estimation of large covariance and precision matrices," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 1-32, February.
    5. 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.
    6. Rothman, Adam J. & Levina, Elizaveta & Zhu, Ji, 2009. "Generalized Thresholding of Large Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 177-186.
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