Anna Skripka is a Michler Scholar in the department of mathematics at Cornell University. From her webpage: "I mainly work on development of methods of high-dimensional and infinite-dimensional noncommutative analysis for problems arising in mathematical physics, noncommutative geometry, applied matrix analysis, and, more recently, statistical estimation."
Talk: MSE bounds for plug-in estimators of matrix functions
Abstract: We show that the mean squared error of the plug-in estimator of a function f(A) of any Hermitian matrix A is controlled by the MSE of the respective estimator of A. The ratio of the two risks is bounded by a suitable modification of the Lipschitz seminorm of f and holds for a large class of functions including Lipschitz functions. When A is a population covariance matrix and its estimator is based on a sample covariance matrix (for instance, a convex banded estimator), the aforementioned property ensures that the number of samples needed to achieve a small MSE of the plug-in estimator of f(A) is on the same scale as the number of samples needed to achieve a small MSE of the estimator of A.