Moderate deviations in subsampling distribution estimation

Abstract

In Politis and Romano (1994) the subsampling methodology was put forth for approximating the sampling distribution (and the corresponding quantiles) of general statistics from i.i.d. and stationary data. In this note, we address the question of how well the subsampling distribution approximates the tail of the target distribution. In the regular setting of the sample mean of an m m -dependent sequence we show a moderate deviation property of the subsampling distribution.