Regularized Generalized Empirical Likelihood Estimators

Mardi | 2017-03-14
16h00-17h20 salle des thèses


Generalized Empirical Likelihood (GEL) estimators are solved by converting a high dimensional primal optimization problem into a dual Minimum Discrepancy problem with fewer parameters. When the GEL problem is subject to a continuum of restrictions, the duality relationships break down as the system of constraints becomes ill-posed. Duality is restored by solving a relaxed problem that leads to a family of Regularized GEL (RGEL) estimators. We show that the RGEL estimator is asymptotically normally distributed and efficient. An implementation strategy in one step inspired from the Three-Steps Empirical Likelihood of Antoine, Bonnal and Renault (2007) is proposed. Monte Carlo simulations based on a linear heteroskedastic model shows that the RGEL and the efficient two-steps CGMM of Carrasco and Florens (2000) have quite similar performances. However, the optimal regularization parameter of the RGEL converges to zero at a slower rate than the one of the CGMM estimator.