To “ on the Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions

co(A): the convex hull of a set A, supp(Q): the support of a measure Q ∈ M, suppP(g(X θ)): the support of g(X θ) when X is distributed according to P ∈ M, s(Q θ): the dimension of the co(suppP(g(X θ))). The principal challenge in deriving our optimality result is establishing part (a) of Theorem 3.1. For ease of exposition, we provide an outline of the proof of this claim before its formal derivation: Step 1. First we note that Λ1(η)⊆ Λ̈1(η), where for M̈0(Q)= { P ∈ M :P Q Q P s(Q θ)=m EP[g(X θ)] = 0 for some θ ∈Θ}