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
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
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