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Consider a family of distributions with parameter θ and monotone likelihood ratio in a statistic T .We learned how to find a uniformly most powerful level α0 test δc of the null hypothesis H0,c : θ ≤ c versus H1,c :θ > c for every c. We also know that these tests are equivalent to a coefficient 1− α0 confidence interval, where the confidence interval contains c if and only if δc does not reject H0, c. The confidence interval is called uniformly most accurate coefficient 1− α0. Based on the equivalence of the tests and the confidence interval, figure out what the definition of “uniformly most accurate coefficient 1− α0” must be. Write the definition in terms of the conditional probability that the interval covers θ1 given that θ = θ2 for various pairs of values θ1 and θ2. |
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