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