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,
then δ0 is inadmissible and dominated by δ for if 0 ≤ α ≤ 1.
c. Apply to the case where and