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

DOI10.3150/21-BEJ1336arXiv2102.04923MaRDI QIDQ6360224

Zhuo-Song Zhang, Qi-Man Shao

Publication date: 9 February 2021

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.

Mathematics Subject Classification ID

Parametric inference (62Fxx) Statistical distribution theory (62Exx)

This page was built for publication: Berry--Esseen Bounds for Multivariate Nonlinear Statistics with Applications to M-estimators and Stochastic Gradient Descent Algorithms

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6360224)