Suppose {P} is q.m.d. at 0. Show P0+h{x : p0 (x) = 0} = o(|h| 2 )

Suppose {Pθ} is q.m.d. at θ0. Show Pθ0+h{x : pθ0 (x) = 0} = o(|h|

2

)

as |h| → 0. Hence, if X1,..., Xn are i.i.d. with likelihood ratio Ln,h defined by

(14.12), show that Pn

θ0+hn−1/2 {Ln,h = ∞} → 0 .