Speaker: Tudor Manole

Abstract: I will recall some classical ideas (https://link.springer.com/content/pdf/10.1007/s004409970006.pdf) for deriving minimax estimation rates for nonsmooth functionals, via polynomial approximation and moment matching. My emphasis will be on the problem of estimating the L^1 distance between discrete distributions (https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=8379458). We'll then see how these ideas can be used to derive minimax lower bounds for estimating the Wasserstein distance between arbitrary distributions (https://projecteuclid.org/journals/bernoulli/volume-28/issue-4/Estimation-of-Wasserstein-distances-in-the-Spiked-Transport-Model/10.3150/21-BEJ1433.short).