Prove Theorem 9.1.3. In Theorem 9.1.3. One-Sided Confidence Intervals from One-Sided Tests. Let X = (X1, .
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In Theorem 9.1.3.
One-Sided Confidence Intervals from One-Sided Tests. Let X = (X1, . . . , Xn) be a random sample from a distribution that depends on a parameter θ. Let g(θ) be a real-valued function, and suppose that for each possible value g0 of g(θ), there is a level α0 test δg0 of the hypotheses (9.1.19). For each possible value x of X, define ω(x) by Eq. (9.1.14). Let γ = 1− α0. Then the random set ω(X) satisfies Eq. (9.1.15) for all θ0 ∈ Ω.
Distribution
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Probability And Statistics
ISBN: 9780321500465
4th Edition
Authors: Morris H. DeGroot, Mark J. Schervish
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