A multivariate CLT for < > 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

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arXiv · 2112.05815

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

Sagak A. Ayvazyan·Vladimir V. Ulyanov

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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.

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Sagak A. Ayvazyan, Vladimir V. Ulyanov. 2021-12-10. A multivariate CLT for < > weighted sums with rate of convergence of order O(1/n). https://doi.org/10.1007/978-3-031-30114-8_6

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