Translator Disclaimer
August 2022 Berry–Esseen bounds for multivariate nonlinear statistics with applications to M-estimators and stochastic gradient descent algorithms
Qi-Man Shao, Zhuo-Song Zhang
Author Affiliations +
Bernoulli 28(3): 1548-1576 (August 2022). DOI: 10.3150/21-BEJ1336

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.

Funding Statement

The first author was partially supported by NSFC12031005 and Shenzhen Outstanding Talents Training Fund and also by Hong Kong RGC GRF 14302515 and 14304917.
The second author was partially supported by Singapore Ministry of Education Academic Research Fund MOE 2018-T2-076.

Citation

Download Citation

Qi-Man Shao. Zhuo-Song Zhang. "Berry–Esseen bounds for multivariate nonlinear statistics with applications to M-estimators and stochastic gradient descent algorithms." Bernoulli 28 (3) 1548 - 1576, August 2022. https://doi.org/10.3150/21-BEJ1336

Information

Received: 1 September 2020; Published: August 2022
First available in Project Euclid: 25 April 2022

Digital Object Identifier: 10.3150/21-BEJ1336

Keywords: averaged stochastic gradient descent algorithms , Berry–Esseen bound , M-estimators , Multivariate normal approximation , randomized concentration inequality , Stein’s method

JOURNAL ARTICLE
29 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.28 • No. 3 • August 2022
Back to Top