Establish the representation formula (8.2.3) and check the equalities in.

Show that the estimators δCZ proposed in Section 8.2 in a Poisson framework are indeed generalized Bayes estimators by exhibiting the corresponding prior distributions.

(Berger (1982b)) Consider x distributed according to 

For  Given two positive differentiable functions, m0 and d, define

a. Show that, under quadratic loss,

under some regularity conditions including

b. Assume that one of the two functions

is finite on [a, b]. Denote this function by gi. Show that if, in addition,

And 

then δis inadmissible and dominated by δ for   if 0 ≤ α ≤ 1.

c. Apply to the case where   and

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