Abstract

Let n be a positive integer and Y(i, j), i, j = 1, ..., n, be random variables with finite fourth moments. Let ? be a random
permutation on {1, ..., n} which independent of Y(i, j)’s. In this paper, we use Stein’s method and the technique from
(Laipaporn, K., 2008) to give a uniform bound in a combinatorial central limit theorem of W =
n *i=1
Y(i, ?(i)). For a
sufficient large n, we yield the rate
27.72
?n
. This constant is better than the result in (Neammanee, K., 2005).
Keywords: Uniform bound, Combinatorial central limit theorem, Stein’s method, Random permutation

This work is licensed under a Creative Commons Attribution 4.0 License.