7.25 Theorem 9.3 Under the conditions of Theorem 9.2, if, in addition (i) E0 t (X,...

7.25 Theorem 9.3 Under the conditions of Theorem 9.2, if, in addition

(i) Eθ0

∂

∂t ψ(X, t)|t=t0

!

is finite and nonzero,

(ii) Eθ0

ψ2(X, t0)

!

< ∞, then

√n(T0 − t0) L

→ N(0, σ2 T0

), where σ2 T0 = Eθ0

ψ2(X, t0)

!

/(Eθ0

∂

∂t ψ(X, t)|t=t0

!

)

2.

[Note that this is a slight generalization of (7.27).]

[Hint: The assumptions on ψ are enough to adapt the Taylor series argument of Theorem 3.10, where ψ takes the place of l



.]