Assume X1,...,Xn are i.i.d. according to a family {P} which is q.m.d. at 0. Suppose, for some

Assume X1,...,Xn are i.i.d. according to a family {Pθ} which is q.m.d. at θ0. Suppose, for some statistic Tn = Tn(X1,...,Xn) and some function µ(θ) assumed differentiable at θ0, n1/2(Tn − µ(θn)) d

→ N(0, σ2) under θn whenever θn = θ0 + hn−1/2. Show the same result holds, first whenever h is replaced by hn → h, and then whenever n1/2(θn − θ0) = O(1).