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

For each n, k is an element of N, let Y-i = (Y-i1, Y-i2 ,..., Y-ik), i = 1, 2,..., n, be independent random vectors in R-k such that Y-ij are independent for all j = 1, 2,..., 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.