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QUESTION
Given W as the estimator of parameter . show that mean square error, MSE (W)=E[(W- )^2] = Var(W)+[Bias(W)]^2.
Given W as the estimator of parameter Ɵ. show that mean square error, MSE (W)=E[(W-Ɵ)^2] = Var(W)+[Bias(W)]^2.
Let W be an estimatorMSE(W) =E [(W-θ)2]= E[(W-E(W)+E(W)- θ2]=E[(W-E(W))2+(E(W)- θ)2+(W-E(W)(E(W)- θ)]=E[(W-E(W))2]+E[(E(W)- θ)2]+E[(W-E(W))(E(W)- θ)]=E[(W-E(W))2]+(E(W)-...