Abstract
Let (P ϑ : ϑ eR p ) be a simple shift family of distributions onR p , and letK ⊂R p be a convex cone. Within the class of nonrandomized tests ofK versusR p ∖K, whose acceptance regionA satisfiesA=A+K, a test with minimal bias is constructed. This minimax test is compared to a likelihood ratio type test, which is optimal with respect to a different criterion. The minimax test is mimicked in the context of linear regression and one-sided tests for covariance matrices.
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