English

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 R\mathbb R. 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}
}
R2 v1 2026-06-22T06:54:26.116Z