Double shrinkage estimators for large sparse covariance matrices

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Covariance matrices play an important role in many multivariate techniques and hence a good covariance estimation is crucial in this kind of analysis. In many applications a sparse covariance matrix is expected due to the nature of the data or for simple interpretation. Hard thresholding, soft thresholding, and generalized thresholding were therefore developed to this end. However, these estimators do not always yield well-conditioned covariance estimates. To have sparse and well-conditioned estimates, we propose doubly shrinkage estimators: shrinking small covariances towards zero and then shrinking covariance matrix towards a diagonal matrix. Additionally, a richness index is defined to evaluate how rich a covariance matrix is. According to our simulations, the richness index serves as a good indicator to choose relevant covariance estimator.

Original language English 1497-1511 15 Journal of Statistical Computation and Simulation 85 8 https://doi.org/10.1080/00949655.2013.873042 Published - 2015 May 24

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Shrinkage Estimator
Sparse matrix
Covariance matrix
Thresholding
Shrinking
Covariance Estimation
Estimator
Diagonal matrix
Estimate
Choose
Shrinkage estimator
Evaluate
Zero
Simulation

All Science Journal Classification (ASJC) codes

• Statistics and Probability
• Modelling and Simulation
• Statistics, Probability and Uncertainty
• Applied Mathematics

Cite this

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abstract = "Covariance matrices play an important role in many multivariate techniques and hence a good covariance estimation is crucial in this kind of analysis. In many applications a sparse covariance matrix is expected due to the nature of the data or for simple interpretation. Hard thresholding, soft thresholding, and generalized thresholding were therefore developed to this end. However, these estimators do not always yield well-conditioned covariance estimates. To have sparse and well-conditioned estimates, we propose doubly shrinkage estimators: shrinking small covariances towards zero and then shrinking covariance matrix towards a diagonal matrix. Additionally, a richness index is defined to evaluate how rich a covariance matrix is. According to our simulations, the richness index serves as a good indicator to choose relevant covariance estimator.",
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In: Journal of Statistical Computation and Simulation, Vol. 85, No. 8, 24.05.2015, p. 1497-1511.

Research output: Contribution to journalArticle

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AU - Chang, Sheng-Mao

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Y1 - 2015/5/24

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