@inproceedings{1d0caed022374e4ebdcdb7ab4dcbc514,
title = "Volume ratio, sparsity, and minimaxity under unitarily invariant norms",
abstract = "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.",
author = "Zongming Ma and Yihong Wu",
year = "2013",
doi = "10.1109/ISIT.2013.6620382",
language = "English (US)",
isbn = "9781479904464",
series = "IEEE International Symposium on Information Theory - Proceedings",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "1027--1031",
booktitle = "2013 IEEE International Symposium on Information Theory, ISIT 2013",
address = "United States",
note = "2013 IEEE International Symposium on Information Theory, ISIT 2013 ; Conference date: 07-07-2013 Through 12-07-2013",
}