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 language | English (US) |
|---|---|
| Pages (from-to) | 1480-1491 |
| Number of pages | 12 |
| Journal | Journal of the American Statistical Association |
| Volume | 107 |
| Issue number | 500 |
| DOIs | |
| State | Published - Dec 1 2012 |
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All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
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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 journal › Article
TY - JOUR
T1 - Positive-definite l1-penalized estimation of large covariance matrices
AU - Xue, Lingzhou
AU - Ma, Shiqian
AU - Zou, Hui
PY - 2012/12/1
Y1 - 2012/12/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84871968656&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84871968656&partnerID=8YFLogxK
U2 - 10.1080/01621459.2012.725386
DO - 10.1080/01621459.2012.725386
M3 - Article
AN - SCOPUS:84871968656
VL - 107
SP - 1480
EP - 1491
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
SN - 0162-1459
IS - 500
ER -