8.12 Suppose that kn[n g()] tends in law to a continuous limit distribution H. Prove that:...

8.12 Suppose that kn[δn − g(θ)] tends in law to a continuous limit distribution H. Prove that:

(a) If k

n/kn → d = 0 or ∞, then k

n[δn − g(θ)] also tends to a continuous limit distribution.

(b) If k

n/kn → 0 or ∞, then k

n[δn − g(θ)] tends in probability to zero or infinity, respectively.

(c) If kn → ∞, then δn → g(θ) in probability.