Statistica Sinica

Tze Leung Lai and Julia Qizhi Wang

Abstract:Edgeworth expansions are developed for a general class of symmetric statistics. Applications of the results are given to obtain approximations to the sampling distributions of statistics in the random censorship model and of linear combinations of order statistics. In addition, Edgeworth expansions are also developed for the bootstrap distributions of these symmetric statistics, showing that the bootstrap approximations are accurate to the order ofO(_{p}n^{-1}).

Key words and phrases:Efron-Stein ANOVA decomposition, asymptoticU-statis- tics, Edgeworth expansions, bootstrap, random censorship model, cumulative hazard function, log-rank statistics, linear combinations of order statistics.