8.8 (a) If n is consistent for , and g is continuous, then g(n) is consistent for...

8.8

(a) If δn is consistent for θ, and g is continuous, then g(δn) is consistent for g(θ).

(b) Let X1,...,Xn be iid as N(θ , 1), and let g(θ) = 0 if θ = 0 and g(0) = 1. Find a consistent estimator of g(θ).