TY - GEN
T1 - Estimation of high dimensional covariance matrices by shrinkage algorithms
AU - Li, Jianbo
AU - Zhou, Jie
AU - Zhang, Bin
AU - Rong Li, X.
N1 - Publisher Copyright:
© 2017 International Society of Information Fusion (ISIF).
PY - 2017/8/11
Y1 - 2017/8/11
N2 - This paper addresses the shrinkage estimation problem of high-dimensional covariance matrices with low sample size data. A class of structured target matrices that include banding, thresholding, diagonal and block diagonal matrices is proposed, and an optimal oracle shrinkage coefficient is derived. To approximate the oracle estimator, an iterative method is presented and proved to be convergent. Moreover, a closed-form solution of its limit, which is guaranteed to be in the unit interval, is obtained. For the banding and thresholding target matrices with unknown bandwidth and threshold respectively, two adaptive algorithms are presented to estimate the covariance matrix, and some properties on the estimation error are discussed theoretically. Some simulations are given to illustrate the competitive performances of proposed covariance matrix estimators.
AB - This paper addresses the shrinkage estimation problem of high-dimensional covariance matrices with low sample size data. A class of structured target matrices that include banding, thresholding, diagonal and block diagonal matrices is proposed, and an optimal oracle shrinkage coefficient is derived. To approximate the oracle estimator, an iterative method is presented and proved to be convergent. Moreover, a closed-form solution of its limit, which is guaranteed to be in the unit interval, is obtained. For the banding and thresholding target matrices with unknown bandwidth and threshold respectively, two adaptive algorithms are presented to estimate the covariance matrix, and some properties on the estimation error are discussed theoretically. Some simulations are given to illustrate the competitive performances of proposed covariance matrix estimators.
KW - High dimension
KW - covariance matrix
KW - shrinkage algorithms
KW - structured target matrices
UR - https://www.scopus.com/pages/publications/85029443494
U2 - 10.23919/ICIF.2017.8009753
DO - 10.23919/ICIF.2017.8009753
M3 - 会议稿件
AN - SCOPUS:85029443494
T3 - 20th International Conference on Information Fusion, Fusion 2017 - Proceedings
BT - 20th International Conference on Information Fusion, Fusion 2017 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 20th International Conference on Information Fusion, Fusion 2017
Y2 - 10 July 2017 through 13 July 2017
ER -