Consider the FayHerriot model in (14.5). Suppose that Ïd , Ï2 v , and β are known.

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

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

Transcribed Image Text:

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