Some Characterizations of Strong Laws for Linear Functions of Order Statistics

Abstract

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.