MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top


For the univariate central limit theorem, the Berry-Esseen theorem gives a quantitative bound on the rate of convergence of distributions to the Normal distribution under Kolmogorov distance:

Are similar statements known for the multivariate version of the central limit theorem, that use some standard distance measure?

This question is a re-post from


share|cite|improve this question
up vote 6 down vote accepted

There is a bunch of such statements which can be obtained by Stein's method.

You might be interested in the paper "On the Rate of Convergence in the Multivariate CLT" by Gotze, which is specifically devoted to Berry-Esseen theorems in the multidimensional setting. Have a look also at the very recent book Normal Approximation by Stein's Method by Chen, Goldstein and Shao.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.