TY - GEN
T1 - Volume ratio, sparsity, and minimaxity under unitarily invariant norms
AU - Ma, Zongming
AU - Wu, Yihong
PY - 2013
Y1 - 2013
N2 - This paper presents a non-asymptotic study of the minimax estimation of high-dimensional mean and covariance matrices. Based on the convex geometry of finite-dimensional Banach spaces, we develop a unified volume ratio approach for determining minimax estimation rates of unconstrained mean and covariance matrices under all unitarily invariant norms. We also establish the rate for estimating mean matrices with group sparsity, where the sparsity constraint introduces an additional term in the rate whose dependence on the norm differs completely from the rate of the unconstrained counterpart.
AB - This paper presents a non-asymptotic study of the minimax estimation of high-dimensional mean and covariance matrices. Based on the convex geometry of finite-dimensional Banach spaces, we develop a unified volume ratio approach for determining minimax estimation rates of unconstrained mean and covariance matrices under all unitarily invariant norms. We also establish the rate for estimating mean matrices with group sparsity, where the sparsity constraint introduces an additional term in the rate whose dependence on the norm differs completely from the rate of the unconstrained counterpart.
UR - http://www.scopus.com/inward/record.url?scp=84890416393&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84890416393&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2013.6620382
DO - 10.1109/ISIT.2013.6620382
M3 - Conference contribution
AN - SCOPUS:84890416393
SN - 9781479904464
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1027
EP - 1031
BT - 2013 IEEE International Symposium on Information Theory, ISIT 2013
T2 - 2013 IEEE International Symposium on Information Theory, ISIT 2013
Y2 - 7 July 2013 through 12 July 2013
ER -