Quantiles as minimizers
Statistics Theory
2014-11-12 v1 Statistics Theory
Abstract
A real random variable admits median(s) and quantiles. These values minimize convex functions on . We show by "Convex Analysis" arguments that the function to be minimized is very natural. The relationship with some notions about functions of bounded variation developed by J.J.~Moreau is emphasized.
Keywords
Cite
@article{arxiv.1411.2732,
title = {Quantiles as minimizers},
author = {Michel Valadier},
journal= {arXiv preprint arXiv:1411.2732},
year = {2014}
}