Bias/Unbiased Estimators and Mean Square Error (MSE) Let X1, X2, . . . , Xn be iid pois(λ) random variables. Recall E(Xi) = λ and var(Xi) = λ. Consider three estimators of λ: λˆ 1 = X1+2X2 3 , λˆ 2 = Xn, λˆ 3 = 5
(a) Calculate the expected value of each estimator. Which estimators are biased and which are unbiased? (b) Calculate the variance of each estimator. (c) Give the Mean Square Error of each estimator. Recall: MSE( ˆθ) can be written as {E( ˆθ) − θ} 2 + V ar( ˆθ). (d) In your opinion, which one of the three estimators do you think is "best"? Provide reasons for your answer.