Generalized Association, with Applications in Multivariate Statistics

Open Access

1 January 1981

journal article
Published by Institute of Mathematical Statistics in The Annals of Statistics

Vol. 9 (1) , 168-176
https://doi.org/10.1214/aos/1176345343

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.

Keywords

ASSOCIATION OF RANDOM VARIABLES
GENERALIZATION OF ASSOCIATION
ABSOLUTE VALUE
UNIMODAL
SYMMETRIC
MULTIVARIATE NORMAL
MIXTURE OF DISTRIBUTIONS
SIMULTANEOUS COMPARISONS
MULTIPLE DECISION PROBLEMS
ANALYSIS OF VARIANCE
STOCHASTIC COMPARISON
MOVING SET INEQUALITIES
SIDAK INEQUALITIES
PARTIAL ORDERNING

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