In Section 9.3wc emphasized the notion of most efficient estimator by comparing the variance of two unbiased
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In Section 9.3wc emphasized the notion of "most efficient estimator" by comparing the variance of two unbiased estimators Θ1 and Θ2. However this does not take into account bias in case one or both estimators are not unbiased. Consider the quantity MSE = E(Θ - θ), where MSE denotes mean squared error. The MSE is often used to compare two estimator’s Θ1 and Θ2 of 6 when either or both is unbiased because (i) it is intuitively reasonable and (ii) it accounts for bias. Show that MSE can be written MSE = E [Θ – E(Θ)]2 + [E(Θ – 6)]2 = Var (Θ) + [Bias(Θ)]2.
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