Title: Empirical likelihood for general conditional estimating equations
Authors: Valentin Patilea - CREST-Ensai (France) [presenting]
Matthieu Marbac - CREST - ENSAI (France)
Abstract: The empirical likelihood (EL) is a prominent statistical inference approach that has extensively studied over the last two decades. Its fast and still ongoing development is due to some important features guaranteed by the fact that it combines the flexibility of the nonparametric methods with the effectiveness of the likelihood approach. Meanwhile, many, if not most, statistical models could be written under the form of conditional moment equations. We propose a new approach for EL in general models defined by conditional moments. The method is based on an equivalent characterization of the initial conditional moment restrictions using a set of unconditional moments that is not increasing with the sample size when the dimension of the parameter of interest is fixed. We allow for the presence of a nuisance parameter of infinite dimension and characterize a class of conditional moment equations models for which the likelihood ratio remains asymptotic pivotal chi-square distributed. The class includes many common semiparametric regression models. Some simulation experiments illustrate the effectiveness of our approach.