Abstract
SUMMARY This paper derives a duality result for a general class of hypothesis testing problems in multivariate analysis utilizing the relationship between convex cones and their polar cones together with the properties of minimum norm problems between points and cones in Euclidian space. Special cases of this result yield generalizations of a well-known duality relation in multivariate equality constraints testing. For example, any multivariate inequality constraints test on the parameters of a multivariate normal random vector has an equivalent multivariate one-sided test in terms of the vector of dual variables associated with the constraints. Also, any combination multivariate inequality and equality constraints test has an equivalent combination multivariate one-sided and two-sided test in terms of the vector of dual variables associated with both sets of constraints.
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