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

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.

Transcribed Image Text:

X₁|0 eß iid I (1,7) T(2, 3).