TY - GEN
T1 - An innovative approach for analysing rank deficient covariance matrices
AU - Tucci, Gabriel H.
AU - Wang, Ke
PY - 2012/10/22
Y1 - 2012/10/22
N2 - The estimation of a covariance matrix from an insufficient amount of data is one of the most common problems in fields as diverse as multivariate statistics, wireless communications, signal processing, biology, learning theory and finance. In [13], a new approach to handle rank deficient covariance matrices was suggested. The main idea was to use dimensionality reduction in conjunction with an average over the Stiefel manifold. In this paper we further continue in this direction and consider a few innovative methods that show considerable improvements with respect to more traditional ones such as diagonal loading. One of the methods is called the Ewens estimator and uses a randomization of the sample covariance matrix over all the permutation matrices with respect to the Ewens measure. The techniques used to attack this problem are broad and run from random matrix theory to combinatorics.
AB - The estimation of a covariance matrix from an insufficient amount of data is one of the most common problems in fields as diverse as multivariate statistics, wireless communications, signal processing, biology, learning theory and finance. In [13], a new approach to handle rank deficient covariance matrices was suggested. The main idea was to use dimensionality reduction in conjunction with an average over the Stiefel manifold. In this paper we further continue in this direction and consider a few innovative methods that show considerable improvements with respect to more traditional ones such as diagonal loading. One of the methods is called the Ewens estimator and uses a randomization of the sample covariance matrix over all the permutation matrices with respect to the Ewens measure. The techniques used to attack this problem are broad and run from random matrix theory to combinatorics.
UR - http://www.scopus.com/inward/record.url?scp=84867526083&partnerID=8YFLogxK
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U2 - 10.1109/ISIT.2012.6283987
DO - 10.1109/ISIT.2012.6283987
M3 - Conference contribution
AN - SCOPUS:84867526083
SN - 9781467325790
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2596
EP - 2600
BT - 2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012
T2 - 2012 IEEE International Symposium on Information Theory, ISIT 2012
Y2 - 1 July 2012 through 6 July 2012
ER -