Consider a family of distributions with parameter and

Chapter 9, Problem 25

(choose chapter or problem)

Consider a family of distributions with parameter and monotone likelihood ratio in a statistic T . We learned how to find a uniformly most powerful level 0 test c of the null hypothesis H0,c : c versus H1,c : >c for every c. We also know that these tests are equivalent to a coefficient 1 0 confidence interval, where the confidence interval contains c if and only if c does not reject H0,c. The confidence interval is called uniformly most accurate coefficient 1 0. Based on the equivalence of the tests and the confidence interval, figure out what the definition of uniformly most accurate coefficient 1 0 must be. Write the definition in terms of the conditional probability that the interval covers 1 given that = 2 for various pairs of values 1 and 2.