Open Access
November 2019 A multivariate Berry–Esseen theorem with explicit constants
Martin Raič
Bernoulli 25(4A): 2824-2853 (November 2019). DOI: 10.3150/18-BEJ1072


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.


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Martin Raič. "A multivariate Berry–Esseen theorem with explicit constants." Bernoulli 25 (4A) 2824 - 2853, November 2019.


Received: 1 February 2018; Revised: 1 September 2018; Published: November 2019
First available in Project Euclid: 13 September 2019

zbMATH: 07110113
MathSciNet: MR4003566
Digital Object Identifier: 10.3150/18-BEJ1072

Keywords: Berry–Esseen theorem , explicit constants , Lyapunov bound , multivariate central limit theorem , Stein’s method

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

Vol.25 • No. 4A • November 2019
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