Cone Order Association

Cone order association, which generalizes the notion of association, is defined. For cone order association, functions which are nondecreasing with respect to a cone order, are nonnegatively correlated. Properties and sufficient conditions are developed. The main result yields a necessary and sufficient condition for a normal random vector to be cone order associated. This parallels a result of L. D. Pitt (1982, Ann. Probab.10 495-499). Cone order association has applications, especially in the area of hypothesis testing. An indication of how cone order association is used to establish unbiasedness of tests is given, along with some examples.