Penalized Empirical Likelihood and Growing Dimensional General Estimating Equations

When a parametric likelihood function is not specified for a model, estimating equations provide an instrument for statistical inference. Qin & Lawless (1994) illustrated that empirical likelihood makes optimal use of these equations in inferences for fixed (low) dimensional unknown parameters. In this paper, we study empirical likelihood for general estimating equations with growing (high) dimensionality and propose a penalized empirical likelihood approach for parameter estimation and variable selection. We quantify the asymptotic properties of empirical likelihood and its penalized version, and show that penalized empirical likelihood has the oracle property. The performance of the proposed method is illustrated via several simulated applications and a data analysis.