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Under a multinormal distribution with arbitrary unknown covariance matrix,the main purpose of this paper is to propose a framework to achieve the goal ofreconciliation of Bayesian, frequentist and Fisherian paradigms for theproblems of testing mean against restricted alternatives (closed convex cones).Combining Fisher's fiducial inference and Wald's decision theory viad-admissibility into an unified approach, the goal can then be achieved. Toproceed, the tests constructed via the union-intersection principle arestudied.

Towards an unified theory for testing statistical hypothesis: Multinormal mean with nuisance covariance matrix