Define the GLS estimator and discuss its properties when Ω is known.Why is this estimator sometimes called infeasible GLS? What happens when Ω is unknown? What would the Ω matrix look like for the case of independent sampling with heteroskedastic errors,where var(ui Xi)= ch(Xi)= σ2 ? Since the inverse of the error variance-covariance matrix is needed to compute the GLS estimator,find Ω-1.The textbook shows that the original model Y = Xβ + U will be transformed into = FU,and F = Ω-1.Find F in the above case,and describe what effect the transformation has on the original data.

Question

Define the GLS estimator and discuss its properties when Ω is known.Why is this estimator sometimes called infeasible GLS? What happens when Ω is unknown? What would the Ω matrix look like for the case of independent sampling with heteroskedastic errors,where var(ui  Xi)= ch(Xi)= σ2  ? Since the inverse of the error variance-covariance matrix is needed to compute the GLS estimator,find Ω-1.The textbook shows that the original model Y = Xβ + U will be transformed into  = FU,and  F = Ω-1.Find F in the above case,and describe what effect the transformation has on the original data.

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The Answer of Define the GLS estimator and discuss its properties when Ω is known.Why is this estimator sometimes called infeasible GLS? What happens when Ω is unknown? What would the Ω matrix look like for the case of independent sampling with heteroskedastic errors,where var(ui  Xi)= ch(Xi)= σ2  ? Since the inverse of the error variance-covariance matrix is needed to compute the GLS estimator,find Ω-1.The textbook shows that the original model Y = Xβ + U will be transformed into  = FU,and  F = Ω-1.Find F in the above case,and describe what effect the transformation has on the original data.

Define the GLS Estimator and Discuss Its Properties When Ω