%0 Journal Article
%T Divergence of sample quantiles
%A Reza Hosseini
%J Statistics
%D 2010
%I arXiv
%X We show that the left (right) sample quantile tends to the left (right) distribution quantile at p in [0,1], if the left and right quantiles are identical at p. We show that the sample quantiles diverge almost surely otherwise. The latter can be considered as a generalization of the well-known result that the sum of a random sample of a fair coin with 1 denoting heads and -1 denoting tails is 0 infinitely often. In the case that the sample quantiles do not converge we show that the limsup is the right quantile and the liminf is the left quantile.
%U http://arxiv.org/abs/1005.2781v1