Abstract

We give bounds on multidimensional Berry-Esseen theorem on a set $A_{k}(x)=\{ (w_{1},w_{2}, \ldots, w_{k})\in \mathbb{R}^{k}\mid \displaystyle\sum^{k}_{i=1}w_{i}\leq x \}$ for $x \in \mathbb{R}$ by using the  Berry-Esseen theorem in $\mathbb{R}$. The rates of convergence are $O(n^{-\frac{1}{2}})$. In addition, we give known constants in the bounds of the approximation.

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