Fitting Penalized Estimator for Sparse Covariance Matrix with Left-Censored Data by the EM Algorithm

Shanyi Lin, Qian-Zhen Zheng, Laixu Shang, Ping-Feng Xu () and Man-Lai Tang ()
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Shanyi Lin: School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China
Qian-Zhen Zheng: College of Education, Zhejiang Normal University, Jinhua 321004, China
Laixu Shang: College of Education, Zhejiang Normal University, Jinhua 321004, China
Ping-Feng Xu: Academy for Advanced Interdisciplinary Studies & Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun 130024, China
Man-Lai Tang: Department of Physics, Astronomy and Mathematics, School of Physics, Engineering & Computer Science, University of Hertfordshire, Hertfordshire AL10 9AB, UK

Mathematics, 2025, vol. 13, issue 3, 1-17

Abstract: Estimating the sparse covariance matrix can effectively identify important features and patterns, and traditional estimation methods require complete data vectors on all subjects. When data are left-censored due to detection limits, common strategies such as excluding censored individuals or replacing censored values with suitable constants may result in large biases. In this paper, we propose two penalized log-likelihood estimators, incorporating the L 1 penalty and SCAD penalty, for estimating the sparse covariance matrix of a multivariate normal distribution in the presence of left-censored data. However, the fitting of these penalized estimators poses challenges due to the observed log-likelihood involving high-dimensional integration over the censored variables. To address this issue, we treat censored data as a special case of incomplete data and employ the Expectation Maximization algorithm combined with the coordinate descent algorithm to efficiently fit the two penalized estimators. Through simulation studies, we demonstrate that both penalized estimators achieve greater estimation accuracy compared to methods that replace censored values with constants. Moreover, the SCAD penalized estimator generally outperforms the L 1 penalized estimator. Our method is used to analyze the proteomic datasets.

Keywords: sparse covariance matrix; Expectation Maximization algorithm; penalized estimator; left-censored data (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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