On the Convergence Rate of the SCAD-Penalized Empirical Likelihood Estimator

Abstract

This paper investigates the asymptotic properties of a penalized empirical likelihood estimator for moment restriction models when the number of parameters (p) and/or the number of moment restrictions increases with the sample size. Our main result is that the SCAD-penalized empirical likelihood estimator is √n/P_n-consistent under a reasonable condition on the regularization parameter. Our consistency rate is better than the existing ones. This paper also provides sufficient conditions under which both √n/P_n-consistency and an oracle property are satisfied simultaneously. Our results provide a solid theoretical support to the penalized empirical likelihood estimator of Leng and Tang (2012).

Keywords: Diverging number of parameters, Penalized empirical likelihood, Sparse models

JEL Classification: C14, C52