(a) Discuss the difference between the following two definitions of the notions of the bias and MSE:

(i) E()=0,MSE) = E-0), for all 0 ; == (ii) E()=0*, MSE;0*) = E 0*), where * is the true 0 in . Explain which one makes sense in the context of frequentist estimation and why the other one does not. (b) Consider the simple Normal statistical model with = 0 and the following estima- tors of a 62 = n+1 = = (c) Compare the relative efficiency of these estimators in terms of their MSE and evaluate it for = 1 and n = 100.