On the Convergence Rate of the SCAD-Penalized Empirical Likelihood Estimator
16 Pages Posted: 7 Dec 2017
Date Written: November 29, 2017
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/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 both √n/Pn-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
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