Consider the Bayes model By performing the following steps, obtain the empirical Bayes estimate of . (a)

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Consider the Bayes model

By performing the following steps, obtain the empirical Bayes estimate of θ.

(a) Obtain the likelihood function

(b) Obtain the mle ^β of β for the likelihood m(x|β).

(c) Show that the posterior distribution of Θ given x and ^β is a gamma distribution.

(d) Assuming squared-error loss, obtain the empirical Bayes estimator.

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Introduction To Mathematical Statistics

ISBN: 9780321794710

7th Edition

Authors: Robert V., Joseph W. McKean, Allen T. Craig

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