Bahadur Representation for U-Quantiles of Dependent Data
Statistics Theory
2011-08-19 v3 Probability
Statistics Theory
Abstract
U-quantiles are applied in robust statistics, like the Hodges-Lehmann estimator of location for example. They have been analyzed in the case of independent random variables with the help of a generalized Bahadur representation. Our main aim is to extend these results to U-quantiles of strongly mixing random variables and functionals of absolutely regular sequences. We obtain the central limit theorem and the law of the iterated logarithm for U-quantiles as straightforward corollaries. Furthermore, we improve the existing result for sample quantiles of mixing data.
Cite
@article{arxiv.1004.2581,
title = {Bahadur Representation for U-Quantiles of Dependent Data},
author = {Martin Wendler},
journal= {arXiv preprint arXiv:1004.2581},
year = {2011}
}