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

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

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