A Berry-Esseen Bound for Functions of Independent Random Variables

Abstract

The rate of convergence in the central limit theorem for functions of independent random variables is studied in a unifying approach. The basic result sharpens and extends a theorem of van Zwet. Applications to $U$-, $L$- and $R$-statistics are also given, improving or extending the results of Helmers and van Zwet, Helmers and Huskova, Does and van Es and Helmers.