Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/308593 
Year of Publication: 
2022
Citation: 
[Journal:] Statistical Papers [ISSN:] 1613-9798 [Volume:] 64 [Issue:] 2 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2022 [Pages:] 509-527
Publisher: 
Springer, Berlin, Heidelberg
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.
Subjects: 
Expectile
Skewness
Stop-loss transform
Dispersion order
Dilation order
Dispersive order
Scale measure
Asymptotic relative efficiency
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
Document Version: 
Published Version

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