Positive-definite l1-penalized estimation of large covariance matrices

Lingzhou Xue, Shiqian Ma, Hui Zou

Research output: Contribution to journalArticle

66 Citations (Scopus)

Abstract

The thresholding covariance estimator has nice asymptotic properties for estimating sparse large covariance matrices, but it often has negative eigenvalues when used in real data analysis. To fix this drawback of thresholding estimation, we develop a positive-definite l1- penalized covariance estimator for estimating sparse large covariance matrices. We derive an efficient alternating direction method to solve the challenging optimization problem and establish its convergence properties. Under weak regularity conditions, nonasymptotic statistical theory is also established for the proposed estimator. The competitive finite-sample performance of our proposal is demonstrated by both simulation and real applications.

Original languageEnglish (US)
Pages (from-to)1480-1491
Number of pages12
JournalJournal of the American Statistical Association
Volume107
Issue number500
DOIs
StatePublished - Dec 1 2012

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Positive definite
Covariance matrix
Thresholding
Estimator
Alternating Direction Method
Regularity Conditions
Convergence Properties
Asymptotic Properties
Data analysis
Optimization Problem
Eigenvalue
Simulation
Asymptotic properties
Finite sample
Optimization problem
Eigenvalues
Regularity

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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Positive-definite l1-penalized estimation of large covariance matrices. / Xue, Lingzhou; Ma, Shiqian; Zou, Hui.

In: Journal of the American Statistical Association, Vol. 107, No. 500, 01.12.2012, p. 1480-1491.

Research output: Contribution to journalArticle

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