Sharp bounds on the expectations of L-statistics expressed in the Gini mean difference units |
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Authors: | Paweł Marcin Kozyra |
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Affiliation: | Department of Mathematical Statistics, Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland |
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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. |
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Keywords: | Order statistics L-statistics Expectation Gini mean difference Optimal bound Bernstein polynomials Variation diminishing property. |
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