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,…,x_n) distributed as independent Poisson random variables, 

a. Use a sequence of conjugate priors and Blyth’s method to show that  x_i is an admissible estimator of λ_i under quadratic loss.

b. For  show that

and deduce that   is an inadmissible estimator of λ = (λ₁,…,λ_n).