Statistics 612: Regular Parametric Models and Likelihood Based Inference

I will not describe the underlying assumptions in details. These are the usual sorts of assumptions one makes for parametric models, in order to be able to establish sensible results. See Page 11 of Chapter 3 of Wellner’s notes for a detailed description of the conditions involved. For a multidimensional parametric model {p(x, θ) : θ ∈ Θ ⊂ Rk}, the information matrix I(θ) is given by: I(θ) = Eθ(l̇(X, θ), l̇(X, θ) ) = −Eθ l̈(X, θ) , where l̇(X, θ) = ∂ ∂ θ l(X, θ)