Consider again the conditions of Exercise 2 Let Yn max X1, , Xn and consider the estimator 2(X1, ,Xn) Yn a Determine the M S E R(, 2) for 0 b Show that for n 2, R(, 2) R(, 1) for 0 c Show that for n 3, the estimator 2 dominates the estimator 1 ...

a It follows from the discussion given in Sec 39 that ...

Consider again the conditions of Exercise 2. Let Yn = max{X1, . . . , Xn} and

Question:

Consider again the conditions of Exercise 2. Let Yn = max{X1, . . . , Xn} and consider the estimator δ2(X1, . . . ,Xn) = Yn.
a. Determine the M.S.E. R(θ, δ2) for θ >0.
b. Show that for n = 2, R(θ, δ2) = R(θ, δ1) for θ >0.
c. Show that for n ≥ 3, the estimator δ2 dominates the estimator δ1.