A multivariate CLT for <<typical>> weighted sums with rate of convergence of order O(1/n)
Abstract
The "typical" asymptotic behavior of the weighted sums of independent random vectors in $k$dimensional space is considered. It is shown that in this case the rate of convergence in the multivariate central limit theorem is of order $O(1/n)$. This extends the onedimensional Klartag and Sodin (2011) result.
 Publication:

arXiv eprints
 Pub Date:
 December 2021
 arXiv:
 arXiv:2112.05815
 Bibcode:
 2021arXiv211205815A
 Keywords:

 Mathematics  Probability;
 60F05 (Primary)
 EPrint:
 29 pages