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Berry--Esseen Bounds for Multivariate Nonlinear Statistics with Applications to M-estimators and Stochastic Gradient Descent Algorithms (2102.04923v2)

Published 9 Feb 2021 in math.PR, math.ST, and stat.TH

Abstract: We establish a Berry--Esseen bound for general multivariate nonlinear statistics by developing a new multivariate-type randomized concentration inequality. The bound is the best possible for many known statistics. As applications, Berry--Esseen bounds for M-estimators and averaged stochastic gradient descent algorithms are obtained.