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The "typical" asymptotic behavior of the weighted sums of independent,identically distibuted random vectors in k-dimensional space is considered. Itis shown that under finitnes of fifth absolute moment of an individual term therate of convergence by Edgeworth correction in the multivariate central limittheorem is of order O(1/n^3/2 ). This extends the one-dimensional Bobkov(2020)result.

On short Edgeworth expansions for weighted sums of random vectors