On a Bahadur-?Kiefer representation of von Mises statistic type for intermediate sample quantiles

摘要

We investigate a Bahadur–Kiefer type representation for the p n -th empirical quantile corresponding to a sample of n i.i.d. random vari- ables when p n ∈ (0, 1) is a sequence which, in particular, may tend to zero or one, i.e., we consider the case of in