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Expectile‐based measures of skewness
Author(s) -
Eberl Andreas,
Klar Bernhard
Publication year - 2022
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12518
Subject(s) - quantile , skewness , estimator , mathematics , moment (physics) , measure (data warehouse) , econometrics , inference , statistical inference , asymptotic analysis , asymptotic distribution , statistics , computer science , data mining , artificial intelligence , physics , classical mechanics
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.