Logarithmic Quantile Estimation for Rank Statistics
Methodology
2013-05-13 v1
Abstract
We prove an almost sure weak limit theorem for simple linear rank statistics for samples with continuous distributions functions. As a corollary the result extends to samples with ties, and the vector version of an a.s. central limit theorem for vectors of linear rank statistics. Moreover, we derive such a weak convergence result for some quadratic forms. These results are then applied to quantile estimation, and to hypothesis testing for nonparametric statistical designs, here demonstrated by the c-sample problem, where the samples may be dependent. In general, the method is known to be comparable to the bootstrap and other nonparametric methods (\cite{THA, FRI}) and we confirm this finding for the c-sample problem.
Cite
@article{arxiv.1305.2250,
title = {Logarithmic Quantile Estimation for Rank Statistics},
author = {Manfred Denker and Lucia Tabacu},
journal= {arXiv preprint arXiv:1305.2250},
year = {2013}
}