Constant on a Uniform Berry-Esseen Bound on a Closed Sphere via Stein's Method

Dawud Thongtha

Abstract

For each $n,k \in\mathbb{N}$, let $Y_{i}=(Y_{i1},Y_{i2}, \ldots, Y_{ik}$), $i=1,2,\ldots,n,$ be independent random vectors in $R^{k}$ such that $Y_{ij}$ are independent for all $j=1,2,\ldots,k$. Without assuming the existence of the third moments, a uniform Berry-Esseen bound for multidimensional central limit theorem on a closed sphere is presented in this paper.