1. Let ˆθ be an estimator of θ. Define the mean squared error (MSE) of ˆθ to be ‘

MSE(ˆθ) = E[(ˆθ −θ)(ˆθ −θ)'].

Show that MSE(ˆθ) = Var(ˆθ )+Bias(ˆθ )Bias(ˆθ)' , where Var(ˆθ) = E{[ˆθ −E(ˆθ)][ ˆθ −E(ˆθ)]'}
and Bias(ˆθ) = E(ˆθ) −ˆθ.