(Relative Efficiency) Let E y X X and Var y X where , X is full row rank, and is nonsingular Show that the RLS estimator is not generally efficient relative to the OLS estimator

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Question: (Relative Efficiency) Let E[y | X] = X and Var[y | X] = where , X is full-row rank, and is

(Relative Efficiency) Let E[y | X] = Xβ₀ and Var[y | X] = Ω₀ where β₀ ∈ ℝᵏ, X is full-row rank, and Ω₀ is nonsingular. Show that the RLS estimator βᵣ is not generally efficient relative to the OLS estimator β.

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