Berry--Esseen Bounds for Multivariate Nonlinear Statistics with Applications to M-estimators and Stochastic Gradient Descent Algorithms
Probability
2021-04-02 v2 Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.2102.04923,
title = {Berry--Esseen Bounds for Multivariate Nonlinear Statistics with Applications to M-estimators and Stochastic Gradient Descent Algorithms},
author = {Qi-Man Shao and Zhuo-Song Zhang},
journal= {arXiv preprint arXiv:2102.04923},
year = {2021}
}
Comments
54 pages