1.36 Let X1,...,Xn be iid with distribution P , and suppose n is UMVU for estimating g()...

1.36 Let X1,...,Xn be iid with distribution Pθ , and suppose δn is UMVU for estimating g(θ) on the basis of X1,...,Xn. If there exists n0 and an unbiased estimator

δ0(X1,...,Xn0 ) which has finite variance for all θ, then δn is consistent for g(θ).

[Hint: For n = kn0 (with k an integer), compare δn with the estimator 1

k

{δ0(X1,...,Xn0 ) + δ0(Xn0+1,...,X2n0 ) + ...}].