Suppose X1, X2, . . . , Xn are iid with pdf f(x|θ) = θx^(θ−1) I(0...

Question

Question

Suppose X1, X2, . . . , Xn are iid with pdf f(x|θ) = θx^(θ−1) I(0 ≤ x ≤ 1), θ > 0.

(a) Is − log(X1) unbiased for θ^(−1)?

(b) Find a better estimator than log(X1) in the sense of with smaller MSE.

(c) Is your estimator in part (b) UMVUE? Explain.

Answer 1

Answer #1

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Answer 2

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