On the convergence rate of the SCAD-penalized empirical likelihood estimator

This paper investigates the asymptotic properties of a penalized empirical likelihood estimator for moment restriction models when the number of parameters ( p n ) 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/pn -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 √ n/pn -consistency and an oracle property are satisfied simultaneously. As far as we know, this paper is the first to specify sufficient conditions for both √ n/pn -consistency and the oracle property of the penalized empirical likelihood estimator.