Divergence of sample quantiles
Statistics Theory
2010-05-18 v1 Statistics Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1005.2781,
title = {Divergence of sample quantiles},
author = {Reza Hosseini},
journal= {arXiv preprint arXiv:1005.2781},
year = {2010}
}