Some necessary and sufficient conditions for strong laws of large numbers to hold for certain classes of linear functions of order statistics (L.F. of O.S.) are given. The results are used to extend and complement some sufficient conditions for strong laws for L.F. of O.S. derived by van Zwet [5] and Wellner [6]. Also a moment-like condition almost equivalent to the existence of an absolute $p$th moment is introduced.
Publié le : 1982-11-14
Classification:
Linear functions of order statistics,
strong laws,
moment conditions,
60F15,
62G30
@article{1176993727,
author = {Mason, David M.},
title = {Some Characterizations of Strong Laws for Linear Functions of Order Statistics},
journal = {Ann. Probab.},
volume = {10},
number = {4},
year = {1982},
pages = { 1051-1057},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993727}
}
Mason, David M. Some Characterizations of Strong Laws for Linear Functions of Order Statistics. Ann. Probab., Tome 10 (1982) no. 4, pp. 1051-1057. http://gdmltest.u-ga.fr/item/1176993727/