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Consider a single observation X from the Cauchy distribution with unknown location parameter θ. That is, the p.d.f. of X is
Suppose that it is desired to test the following hypotheses:
H0: θ = 0,
H1: θ >0.
Show that, for every α0 (0 <α0 < 1), there does not exist a UMP test of these hypotheses at level of significance α0. |
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