Empirical Likelihood in Nonparametric and Semiparametric Models

Abstract

We review some recent results on empirical likelihood in nonparametric and semiparametric models. In particular we show the validity of empirical likelihood for Hadamard differentiable functionate tangential to a wellchosen set. We give the basic ingredients for proving its asymptotic validity and Bartlett correctability: convex duality. LAN properties of the empirical likelihood ratio in its dual form and uniform convergence of the empirical process (over classes of discrete probability). Extensions to semiparametric problems with estimated infinite dimensional parameters are also considered. Taking this point of view we revisit and extend some results in biased sampling models.KeywordsEmpirical likelihoodsemiparametric modelsconvexdualityLAN