Suppose X1,..., Xn are i.i.d. according to a model {P : }, where is an

Suppose X1,..., Xn are i.i.d. according to a model {Pθ : θ ∈ }, where is an open subset of Rk

. Assume that the model is q.m.d. Show that there cannot exist an estimator sequence Tn satisfying lim n→∞ sup

|θ−θ0|≤n−1/2 Pn

θ (n1/2

|Tn − θ| > ) = 0 (14.97)

for every > 0 and any θ0. (Here Pn

θ means the joint probability distribution of

(X1,..., Xn) under θ.) Suppose the above condition (14.97) only holds for some

> 0. Does the same conclusion hold?