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Assume that the distribution of x is f (x) = 1/θ, 0 ≤ x ≤ θ. In random sampling from this distribution, prove that the sample maximum is a consistent estimator of θ. Note: You can prove that the maximum is the maximum likelihood estimator of θ. But the usual properties do not apply here. Why not? [Hint: Attempt to verify that the expected first derivative of the log-likelihood with respect to θ is zero.] |
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