Abstract
The problem to obtain the most stringent size-α test ϕ * is formulated as a linear programming problem of type II (Section 2). If sample space and parameter space are finite, then we obtain a discrete linear programming problem (Section 4). The well-known results for this special case, and the results of Krafft and Witting for the maximin size-α test, point out how to formulate the dual problem of type I in the general case and how to develop the corresponding duality theory (Sections 5 and 6). It turns out that ϕ * can be determined completely by the solution of the dual type I problem, which solution may be characterized by means of a least favorable pair $$(\tilde \lambda ,\tilde v)$$ of probability measures over Ω H and Ω K respectively (Section 7). Statistical interpretation shows further that ϕ * can also be characterized by means of a least favorable distribution $$\tilde v$$ over Ω K alone (Section 8).
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