A NOTE ON GENERALIZED EMPIRICAL LIKELIHOOD ESTIMATION OF SEMIPARAMETRIC CONDITIONAL MOMENT RESTRICTION MODELS
提出一种基于经验似然的估计方法，用于包含未知函数的半参数条件矩限制模型，通过筛法近似未知函数，证明了估计量的一致性和渐近正态性。
This paper proposes an empirical likelihood-based estimation method for semiparametric conditional moment restriction models, which contain finite dimensional unknown parameters and unknown functions. We extend the results of Donald, Imbens, and Newey (2003, Journal of Econometrics 117, 55–93) by allowing unknown functions to be included in the conditional moment restrictions. We approximate unknown functions by a sieve method and estimate the finite dimensional parameters and unknown functions jointly. We establish consistency and derive the convergence rate of the estimator. We also show that the estimator of the finite dimensional parameters is $\sqrt n$ -consistent, asymptotically normally distributed, and asymptotically efficient.