Sharp bounds on the expectations of L-statistics expressed in the Gini mean difference units

Paweł Marcin Kozyra and Tomasz Rychlik

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 6, 2921-2941

Abstract: We describe a method of calculating sharp lower and upper bounds on the expectations of arbitrary, properly centered L-statistics expressed in the Gini mean difference units of the original i.i.d. observations. Precise values of bounds are derived for the single-order statistics, their differences, and some examples of L-estimators. We also present the families of discrete distributions which attain the bounds, possibly in the limit.

Date: 2017
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DOI: 10.1080/03610926.2015.1053937

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