The empirical Edgeworth expansion for a studentized trimmed mean

We establish the validity of the empirical Edgeworth expansion (EE) for a studentized trimmed mean, under the sole condition that the underlying distribution function of the observations satisfies a local smoothness condition near the two quantiles where the trimming occurs. A simple explicit formula for the $n^{-1/2$ term (correcting for skewness and bias; $n$ being the sample size) of the EE will be given. In particular our result supplements previous work by Hall and Padmanabhan (1992) and Putter and van Zwet (1998). The proof is based on a U-statistic type approximation and also uses a version of Bahadur's (1966) representation for sample quantiles.