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Extremiles: A New Perspective on Asymmetric Least Squares

Daouia, Abdelaati; Gijbels, Irène; Stupfler, Gilles

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Authors

Abdelaati Daouia

Irène Gijbels

Gilles Stupfler



Abstract

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.

Citation

Daouia, A., Gijbels, I., & Stupfler, G. (2019). Extremiles: A New Perspective on Asymmetric Least Squares. Journal of the American Statistical Association, 114(527), 1366-1381. https://doi.org/10.1080/01621459.2018.1498348

Journal Article Type Article
Acceptance Date Jul 4, 2018
Online Publication Date Jul 18, 2018
Publication Date 2019
Deposit Date Jul 9, 2018
Publicly Available Date Mar 28, 2024
Journal Journal of the American Statistical Association
Print ISSN 0162-1459
Electronic ISSN 1537-274X
Publisher Taylor and Francis
Peer Reviewed Peer Reviewed
Volume 114
Issue 527
Pages 1366-1381
DOI https://doi.org/10.1080/01621459.2018.1498348
Public URL https://nottingham-repository.worktribe.com/output/947216
Publisher URL https://www.tandfonline.com/doi/full/10.1080/01621459.2018.1498348

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