Berry–Esseen bounds for multivariate nonlinear statistics with applications to M-estimators and stochastic gradient descent algorithms-Reference-Cited by-同舟云学术

Berry–Esseen bounds for multivariate nonlinear statistics with applications to M-estimators and stochastic gradient descent algorithms

Published:2022-08-01 Issue:3 Volume:28 Page:
ISSN:1350-7265
Container-title:Bernoulli
language:
Short-container-title:Bernoulli

Author:

Shao Qi-Man¹,Zhang Zhuo-Song²

Affiliation:

1. Department of Statistics and Data Scinece, Southern University of Science and Technology, Shenzhen, Guangdong, P.R. China

2. Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T. Hong Kong

Publisher

Bernoulli Society for Mathematical Statistics and Probability

Subject

Statistics and Probability

Reference32 articles.

1. Vershynin, R. (2012). Introduction to the non-asymptotic analysis of random matrices. In Compressed Sensing 210–268. Cambridge: Cambridge Univ. Press.

2. Anastasiou, A., Balasubramanian, K. and Erdogdu, M.A. (2019). Normal approximation for stochastic gradient descent via non-asymptotic rates of martingale CLT. In Proceedings of the Thirty-Second Conference on Learning Theory. PMLR 99 115–137.

3. Bach, F. and Moulines, E. (2011). Non-asymptotic analysis of stochastic approximation algorithms for machine learning. In Neural Information Processing Systems (NIPS). Spain.

4. Barbour, A.D. (1990). Stein’s method for diffusion approximations. Probab. Theory Related Fields 84 297–322. 10.1007/BF01197887

5. Bentkus, V. (2003). On the dependence of the Berry-Esseen bound on dimension. J. Statist. Plann. Inference 113 385–402. 10.1016/S0378-3758(02)00094-0

Cited by 6 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Berry-Esseen bounds for self-normalized sums of locally dependent random variables;Science China Mathematics;2024-08-26

2. Resampling Stochastic Gradient Descent Cheaply;2023 Winter Simulation Conference (WSC);2023-12-10

3. Adaptive Powerball Stochastic Conjugate Gradient for Large-Scale Learning;IEEE Transactions on Big Data;2023-12

4. Bounds in L1 Wasserstein distance on the normal approximation of general M-estimators;Electronic Journal of Statistics;2023-01-01

5. Asymptotic normality and confidence region for Catoni's Z estimator;Stat;2022-12