Extremile Regression

Abstract

Extremiles are a least squares alternative to quantiles, determined by probability-weighted moments rather than tail probabilities. They benefit from several interpretations and closed form expressions that are equivalent for continuous distributions, and they characterize a distribution just as quantiles do. Their regression versions similarly define a least squares analog of regression quantiles. We give a comprehensive overview of the state of the art regarding probabilistic and statistical properties of unconditional extremiles and their regression counterparts and provide a comparison between extremiles and other important classes of indicators for the description of unconditional and conditional distributions on real data examples.

Replaced by

Abdelaati Daouia, and Gilles Stupfler, “Extremile Regression”, Wiley StatsRef: Statistics Reference Online, n. 24-1546, May 2024, forthcoming.

Reference

Abdelaati Daouia, and Gilles Stupfler, “Extremile Regression”, TSE Working Paper, n. 24-1546, May 2024.