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Expectile-based measures of skewness

Eberl, Andreas; Klar, Bernhard

In the literature, quite a few measures have been proposed for quantifying the deviation of a probability distribution from symmetry. The most popular of these skewness measures are based on the third centralized moment and on quantiles. However, there are major drawbacks in using these quantities. These include a strong emphasis on the distributional tails and a poor asymptotic behavior for the (empirical) moment‐based measure as well as difficult statistical inference and strange behaviour for discrete distributions for quantile‐based measures. Therefore, in this paper, we introduce skewness measures based on or connected with expectiles. Since expectiles can be seen as smoothed versions of quantiles, they preserve the advantages over the moment‐based measure while not exhibiting most of the disadvantages of quantile‐based measures. We introduce corresponding empirical counterparts and derive asymptotic properties. Finally, we conduct a simulation study, comparing the newly introduced measures with established ones, and evaluating the performance of the respective estimators.

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Verlagsausgabe §
DOI: 10.5445/IR/1000131159
Veröffentlicht am 08.04.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2021
Sprache Englisch
Identifikator ISSN: 0303-6898, 1467-9469
KITopen-ID: 1000131159
Erschienen in Scandinavian Journal of Statistics
Verlag Wiley
Schlagwörter expectile; omega ratio; skewness measure; stop‐loss transform
Nachgewiesen in Web of Science
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