We present optimal upper bounds for expectations of order statistics from i.i.d. samples with a common distribution function belonging to the restricted family of probability measures that either precede or follow a given one in the star ordering. The bounds for families with monotone failure density and rate on the average are specified. The results are obtained by projecting functions onto convex cones of Hilbert spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am29-1-3,
author = {Tomasz Rychlik},
title = {Optimal mean-variance bounds on order statistics from families determined by star ordering},
journal = {Applicationes Mathematicae},
volume = {29},
year = {2002},
pages = {15-32},
zbl = {1011.62049},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am29-1-3}
}
Tomasz Rychlik. Optimal mean-variance bounds on order statistics from families determined by star ordering. Applicationes Mathematicae, Tome 29 (2002) pp. 15-32. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am29-1-3/