Statistica Sinica

Qiying Wang and Neville C Weber

Abstract:The leading term in the normal approximation to the distribution of -statistics of degree 2 is derived. This result is applied to establish the exact rate of convergence in the Central Limit Theorem for -statistics and to obtain the one-term Edgeworth expansion for the distribution function. Analogous results for more general -type statistics are also considered.

Key words and phrases:Berry-Esséen theorem, characterisation of rate of convergence, Edgeworth expansion, optimal moments, nonlattice condition, U-statistics, L-statistics.