Let X1, . . . , Xn ∼ iid Beta(θ, 1). (a) Find the UMP test...

Let X1, . . . , Xn ∼ iid Beta(θ, 1). (a) Find the UMP test for H0 : θ ≥ θ0 vs H1 : θ < θ0. (b) Find the corresponding Wald test. (c) How do these tests compare and which would you prefer?

Expert Solution

orchestra answered 1 year ago

Let X1, . . . , Xn ∼ iid Exp(θ) and consider the test for H0...

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Let X1, . . . , Xn ∼ iid N(θ, σ2 ), with one-sided hypotheses H0 : θ ≤ θ0 vs H1 : θ > θ0. (a) If σ^2 is known, we can use the UMP size-α test. Find the formula for the P-value of this test.

Let X1, X2, · · · , Xn be iid samples from density: f(x) = {θx^(θ−1),...

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Let X1,...,Xn ∼ Geo(θ). (a) Find a 90% asymptotic confidence interval for θ. (b) Find a...

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Let X1, . . . , Xn i.i.d. Uniform(θ, θ + 1). Show that: ˆθ1 =...

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