Empirical Likelihood Approach Sample Clauses

Empirical Likelihood Approach. Qin & Xxxxxxx [68] propose an alternative approach for approximating the likelihood ratio, which is based on empirical likelihood. Briefly, let x1, . . . , xn be independent and identically distributed (iid) observations from a d-variate distribution F with an associated p × 1 parameter θ. Although Qin & Xxxxxxx require that x1, . . . , xn be iid observations, this work has been generalized to handle the situation where ob- servations are independent but not identically distributed. This extension requires one to assume that the estimating functions are iid from a super population of esti- mating functions. Thus, for the remainder of this section, we take x1, . . . , xn to be independent observations from F with an associated parameter θ. By definition, the empirical likelihood function is n n L(F ) = ∏ dF (xi) = ∏ pi, i=1 i=1 where pi = dF (xi) = Pr(X = xi). It can be shown that the empirical likelihood function is maximized by the empirical distribution function Fn(x) = 1 ∑n I(xi <