Daouia, Abdelaati, Gijbels, Irene and Stupfler, Gilles Claude (2019) Extremiles: A new perspective on asymmetric least squares. Journal of the American Statistical Association, 114 (527). pp. 1366-1381.

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Identification Number : 10.1080/01621459.2018.1498348


Quantiles and expectiles of a distribution are found to be useful descriptors of its tail in the same way as the median and mean are related to its central behavior. This paper considers a valuable alternative class to expectiles, called extremiles, which parallels the class of quantiles and includes the family of expected minima and expected maxima. The new class is motivated via several angles, which reveals its specific merits and strengths. Extremiles suggest better capability of fitting both location and spread in data points and provide an appropriate theory that better displays the interesting features of long-tailed distributions. We discuss their estimation in the range of the data and beyond the sample maximum. A number of motivating examples are given to illustrate the utility of estimated extremiles in modeling noncentral behavior. There is in particular an interesting connection with coherent measures of risk protection.

Item Type: Article
Language: English
Date: 2019
Refereed: Yes
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 18 Jan 2019 10:20
Last Modified: 04 Sep 2023 07:17
OAI Identifier: oai:tse-fr.eu:33000
URI: https://publications.ut-capitole.fr/id/eprint/26312
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