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Statistics
A Journal of Theoretical and Applied Statistics
Volume 49, 2015 - Issue 2
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Original Articles

Maximal dispersion of order statistics in dependent samples

Pages 386-395 | Received 13 Jul 2013, Accepted 02 Oct 2014, Published online: 24 Nov 2014
 

Abstract

Consider n arbitrarily dependent identically distributed random variables. Rychlik [Extreme variances of order statistics in dependent samples. Statist Probab Lett. 2008;78:1577–1582] proved that the optimal bound for the ratio of variances of the mth order statistic and a single-parent variable is the maximum of n/m and n/(n+1m). We show here that the evaluation is optimal for many other measures of dispersion of the order statistics and original variable.

Mathematics Subject Classification:

Acknowledgements

The author thanks an anonymous referee for suggesting modifications that improved presentation of the results.

Additional information

Funding

The research was supported by the Polish Ministry of Science and Higher Education [grant number N N201 416739].

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