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 and
. 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.