Abstract:
We consider “typical” asymptotic behavior of weighted sums of independent identically distributed random vectors in the $k$-dimensional space. We show that if the fifth absolute moment of a separate term is finite, then in the multidimensional central limit theorem, the convergence rate is $O(1/n^{3/2})$ under the Chebyshev–Edgeworth correction. This result generalizes a result of Bobkov [Edgeworth corrections in randomized central limit theorems, in Geometric Aspects of Functional Analysis, Springer, 2020, pp. 71–97] to the multidimensional case.
Keywords:Chebyshev–Edgeworth expansion, multidimensional central limit theorem, multidimensional Gaussian distribution.
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