Quantiles as minimizers

2014/11/11 by Michel Valadier, Valadier, Michel
Decision Sciences · Mathematics · #Fuzzy Systems and Optimization #Risk and Portfolio Optimization #Statistical Methods and Inference #math.ST #msc:26A #msc:52 #msc:62 #stat.TH

paper · pdf · doi:10.48550/arxiv.1411.2732

arxiv created 2014/11/11 · arxiv updated 2014/11/12

Abstract

A real random variable admits median(s) and quantiles. These values minimize convex functions on \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.

Related

• On semi-continuity and continuity of the smallest and largest minimizing point of real convex functions with applications in probability and statistics
• Medians, Continuity, and Oscillation
• Minimax theorems in a fully non-convex setting
• Quantiles Equivariance
• Quantiles symmetry