SOME RESAMPLING PROCEDURES UNDER SYMMETRY

This paper investigates the properties of bootstrap and related methods assuming that the underlying distribution is symmetric but otherwise unknown. In particular it studies the percentile-t, nonparametric tilting and empirical likelihood and finds that the performance of percentile-t and non-parametric tilting methods can be improved by incorporating the symmetry into the resampling procedure. However, for symmetric empirical likelihood, the Bartlett correctability no longer holds, although use of bootstrap calibration restores the good coverage properties typically associated with Bartlett correction. This surprising result shows that Bartlett correctability is a very delicate property.