Multivariate Normal Approximation by Stein's Method: The Concentration Inequality Approach

Details Multivariate Normal Approximation by Stein's Method: The Concentration Inequality Approach Multivariate Normal Approximation by Stein's Method: The Concentration Inequality Approach

2011-11-17

arxiv.org/abs/1111.4073v1

Mathematics

Probability

25 pages

Scientific paper

The concentration inequality approach for normal approximation by Stein's method is generalized to the multivariate setting. This approach is used to prove a multivariate normal approximation theorem for standardized sums of independent random vectors with an error bound of the order $k^{1/2}\gamma$, where $k$ is the dimension of the random vectors and $\gamma$ is the sum of absolute third moments of the random vectors.

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