Daouia, AbdelaatiORCID: https://orcid.org/0000-0003-2621-8860 and Stupfler, Gilles ClaudeORCID: https://orcid.org/0000-0003-2497-9412 (2024) Extremile Regression. In: Wiley StatsRef‎: statistics reference online Balakrishnan, NarayanaswamyORCID: https://orcid.org/0000-0001-5842-8892, Colton, Theodore, Everitt, Brian Sidney, Piegorsch, Walter W.ORCID: https://orcid.org/0000-0003-2725-5604, Ruggeri, FabrizioORCID: https://orcid.org/0000-0002-7655-6254 and Teugels, Jozef (eds.) John Wiley & Sons. Hoboken ISBN 9781118445112

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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.

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