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.

翻译：我们通过开发新的多变量型随机集中不平等,建立了一个通用多变量非线性非线性统计的Berry-Esseen 框。对于许多已知的统计数据来说,这个框是最好的。 作为应用,我们获得了测算器的Berry-Esseen 界限和平均随机梯度梯度基底算法。