Empirical likelihood in some semiparametric models

Bertail, Patrice

Bernoulli, Tome 12 (2006) no. 2, p. 299-331 / Harvested from Project Euclid

Résumé

We study the properties of empirical likelihood for Hadamard differentiable functionals tangentially to a well chosen set and give some extensions in more general semiparametric models. We give a straightforward proof of its asymptotic validity and Bartlett correctability, essentially based on two ingredients: convex duality and local asymptotic normality properties of the empirical likelihood ratio in its dual form. Extensions to semiparametric problems with estimated infinite-dimensional parameters are also considered. We give some applications to confidence intervals for the location parameter of a symmetric model, M-estimators with some nuisance parameters and general functionals in biased sampling models.

Détail

Publié le : 2006-04-14
Classification:  Bartlett correction,  bias sampling models,  Donsker class,  empirical likelihood,  empirical process,  Hadamard differentiability,  semiparametric models