Estimating the covariance of random matrices

Pierre Youssef (University of Alberta)

Abstract


We extend to the matrix setting a recent result of Srivastava-Vershynin about estimating the covariance matrix of a random vector. The result can be interpreted as a quantified version of the law of large numbers for  positive semi-definite matrices which verify some regularity assumption. Beside giving examples, we discuss the notion of log-concave matrices and give estimates on the smallest and largest eigenvalues of a sum of such matrices.

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Pages: 1-26

Publication Date: December 19, 2013

DOI: 10.1214/EJP.v18-2579

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