Question: Consider the additive random-effects model Xijk = + Ai + Bj + Uijk (i = 1,...,a; j = 1,...,b; k = 1,...,n), where the

Consider the additive random-effects model Xijk = µ + Ai + Bj + Uijk (i = 1,...,a; j = 1,...,b; k = 1,...,n), where the A’s, B’s, and U’s are independent normal with zero means and variances σ2 A, σ2 B, and σ2’ respectively. Determine

(i) the joint density of the X’s,

(ii) the UMP unbiased test of H : σ2 B/σ2 ≤ δ.

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