Description

Let (X1,…,Xn) be a random sample of size n from the uniform distribution on the interval (\theta , \theta + 1) with an unknown \theta in ℜ. A priori nothing is known about \theta , so a non-informative prior distribution \pi (\theta ) = constant is deemed appropriate. Show that the Bayes estimator under the squared-error loss function is a consistent estimator of \theta .

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