Variable selection using penalized empirical likelihood

This paper considers variable selection for moment restriction models. We propose a penalized empirical likelihood (PEL) approach that has desirable asymptotic properties comparable to the penalized likelihood approach, which relies on a correct parametric likelihood specification. In addition to being consistent and having the oracle property, PEL admits inference on parameter without having to estimate its estimator's covariance. An approximate algorithm, along with a consistent BIC-type criterion for selecting the tuning parameters, is provided for PEL. The proposed algorithm enjoys considerable computational efficiency and overcomes the drawback of the local quadratic approximation of nonconcave penalties. Simulation studies to evaluate and compare the performances of our method with those of the existing ones show that PEL is competitive and robust. The proposed method is illustrated with two real examples.