4. In the Gaussian/Gaussian model (5.5), if 2 = 1 and = 0, the Yis are marginally independent with distribution Yi| iid N(0,

4. In the Gaussian/Gaussian model (5.5), if σ2 = 1 and μ = 0, the Yis are marginally independent with distribution Yi|τ iid

∼ N(0, 1 + τ 2) ≡ N(0, 1/B) .

(a) Find the marginal MLE of B, B MLE, and the resulting PEB point estimates ˆθEB i , i = 1,...,k.

(b) Show that while B in (5.25) is not equal to B MLE, it is unbiased for B with respect to m(y|B). Show further that using this B in the usual PEB point estimation fashion produces the James-Stein estimator

(5.23).