English

A multivariate Berry--Esseen theorem with explicit constants

Probability 2019-07-24 v4

Abstract

We provide a Lyapunov type bound in the multivariate central limit theorem for sums of independent, but not necessarily identically distributed random vectors. The error in the normal approximation is estimated for certain classes of sets, which include the class of measurable convex sets. The error bound is stated with explicit constants. The result is proved by means of Stein's method. In addition, we improve the constant in the bound of the Gaussian perimeter of convex sets.

Keywords

Cite

@article{arxiv.1802.06475,
  title  = {A multivariate Berry--Esseen theorem with explicit constants},
  author = {Martin Raič},
  journal= {arXiv preprint arXiv:1802.06475},
  year   = {2019}
}

Comments

30 pages, 1 figure, 1 table

R2 v1 2026-06-23T00:25:58.114Z