Berry–Esseen Bounds for Multivariate Nonlinear Statistics with Applications to M-estimators and Stochastic Gradient Descent Algorithms

02/09/2021

∙

by   Qi-Man Shao, et al.

∙

0

∙

share

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.