Edgeworth Expansions for a Sample Sum from a Finite Set of Independent Random Variables

Abstract

Let $\{X_1,\cdots ,X_N\}$ be a set of $N$ independent random variables, and let $S_n$ be a sum of $n$ random variables chosen without replacement from the set $\{X_1, \cdots , X_N\}$ with equal probabilities. In this paper we give a one-term Edgeworth expansion of the remainder term for the normal approximation of $S_n$ under mild conditions.