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

2021/02/09 by Shao, Qi-Man, Zhang, Zhuo-Song · 5 citations
#62E20 #FOS: Mathematics #Primary 60F05 #Probability (math.PR) #Statistics Theory (math.ST) #secondary 62F12

paper · doi:10.48550/arxiv.2102.04923

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.

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