A multivariate CLT for <<typical>> weighted sums with rate of convergence of order O(1/n)

Sagak A. Ayvazyan; Vladimir V. Ulyanov

doi:10.1007/978-3-031-30114-8_6

paper

A multivariate CLT for <<typical>> weighted sums with rate of convergence of order O(1/n)

arXiv:2112.05815 · doi:10.1007/978-3-031-30114-8_6

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 one-dimensional Klartag and Sodin (2011) result.

29 pages