Generalized Association, with Applications in Multivariate Statistics

Abstract

Association of random variables [Ann. Math. Statist. 38 1466-1474] is generalized by considering increasing functions on certain partially ordered spaces. Generalized association enjoys many of the basic properties possessed by association. An essential connection links the two notions. Generalized association is inherited under certain mixing processes. Applications of this result follow for absolute value ordering, unimodal ordering, and linear ordering of the real numbers.