Let V1, ,Vn be independently distributed as N(0, 1), and given V1 v1, , Vn vn, let Xi (i 1, ,n) be independently distributed as N(vi, 1) (i) There does not exist a UMP test of H 0 against K 0 (ii) There does exist a UMP conditional test of H against K given the ancillary (V1, ,Vn) Buehler (1982) ...

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Let V1,...,Vn be independently distributed as N(0, 1), and given V1 = v1,..., Vn = vn, let

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Let V1,...,Vn be independently distributed as N(0, 1), and given V1 = v1,..., Vn = vn, let Xi (i = 1,...,n) be independently distributed as N(θvi, 1).

(i) There does not exist a UMP test of H : θ = 0 against K : θ > 0.

(ii) There does exist a UMP conditional test of H against K given the ancillary

(V1,...,Vn). [Buehler (1982).]

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Testing Statistical Hypotheses

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Let V1,...,Vn be independently distributed as N(0, 1), and given V1 = v1,..., Vn = vn, let

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