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Stochastic orders and measures of skewness and dispersion based on expectiles

Eberl, Andreas ORCID iD icon 1; Klar, Bernhard ORCID iD icon 1
1 Institut für Stochastik (STOCH), Karlsruher Institut für Technologie (KIT)

Abstract:

Recently, expectile-based measures of skewness akin to well-known quantile-based skewness measures have been introduced, and it has been shown that these measures possess quite promising properties (Eberl and Klar in Comput Stat Data Anal 146:106939, 2020; Scand J Stat, 2021, https://doi.org/10.1111/sjos.12518). However, it remained unanswered whether they preserve the convex transformation order of van Zwet, which is sometimes seen as a basic requirement for a measure of skewness. It is one of the aims of the present work to answer this question in the affirmative. These measures of skewness are scaled using interexpectile distances. We introduce orders of variability based on these quantities and show that the so-called weak expectile dispersive order is equivalent to the dilation order. Further, we analyze the statistical properties of empirical interexpectile ranges in some detail.


Verlagsausgabe §
DOI: 10.5445/IR/1000148166
Veröffentlicht am 10.02.2023
Originalveröffentlichung
DOI: 10.1007/s00362-022-01331-x
Scopus
Zitationen: 3
Web of Science
Zitationen: 3
Dimensions
Zitationen: 6
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2023
Sprache Englisch
Identifikator ISSN: 0932-5026, 0039-0631, 1613-9798
KITopen-ID: 1000148166
Erschienen in Statistical Papers
Verlag Springer
Band 64
Heft 2
Seiten 509–527
Vorab online veröffentlicht am 11.06.2022
Nachgewiesen in Web of Science
Dimensions
Scopus
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