Expectiles and M-quantiles are quantiles

Jones, M. C. (1994). Expectiles and M-quantiles are quantiles. Statistics and Probability Letters, 20(2) pp. 149–153.

DOI: https://doi.org/10.1016/0167-7152(94)90031-0

Abstract

Expectiles and M-quantiles are related to means and M-estimates of location in the same way as quantiles are related to the median. We show that expectiles and certain M-quantiles of a distribution F are precisely the ordinary quantiles of distributions G related by an explicit formula to F.

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