Moment Selection and Generalized Empirical Likelihood Estimation in High-Dimensional Unconditional Moment Conditions

This paper investigates the moment selection and parameter estimation problem of high-dimensional unconditional moment conditions. First, the authors propose a Fantope projection and selection (FPS) approach to distinguish the informative and uninformative moments in high-dimensional unconditional moment conditions. Second, for the selected unconditional moment conditions, the authors present a generalized empirical likelihood (GEL) approach to estimate unknown parameters. The proposed method is computationally feasible, and can efficiently avoid the well-known ill-posed problem of GEL approach in the analysis of high-dimensional unconditional moment conditions. Under some regularity conditions, the authors show the consistency of the selected moment conditions, the consistency and asymptotic normality of the proposed GEL estimator. Two simulation studies are conducted to investigate the finite sample performance of the proposed methodologies. The proposed method is illustrated by a real example.