Consider the FayHerriot model in (14.5). Suppose that d , 2 v , and are known.

Consider the Fay–Herriot model in (14.5). Suppose that ψd , σ2 v , and β are known.
a. Let

With a ∈ [0, 1]. Show that, under the model in (14.5), EM [˜θd (a) −θd ] = 0 for any a ∈ [0, 1].
b. Show that VM [˜θd (a)−θd ] is minimized when a = αd and that VM [˜θd (αd )−θd ] = αdψd . Consequently, under the model, VM [˜θd (αd ) − θd ] ≤ VM[d − θd ].