Verify that the three conditions of Lemma 8.3.3 are actually satisfied in the case of a quadratic loss,
for every positive-definite matrix Q.
(Clevenson and Zidek (1975)) Consider (x1,…,xn) distributed as independent Poisson random variables,
a. Use a sequence of conjugate priors and Blyth’s method to show that xi is an admissible estimator of λi under quadratic loss.
b. For show that
and deduce that is an inadmissible estimator of λ = (λ1,…,λn).