Cross-fitted empirical likelihood on semiparametric models
提出一种交叉拟合经验似然方法，用于在复杂高维干扰参数存在时对低维参数进行推断，模拟和实验表明其比Wald方法覆盖更准确。
Summary We propose a new cross-fitted empirical likelihood (CFEL) inference procedure for low-dimensional parameters in the presence of complex, infinite dimensional nuisance parameters that may be estimated by modern machine-learning methods. Relying on the Neyman orthogonal moment condition and cross-fitting as a sample-splitting procedure, we show that our CFEL statistic is asymptotically pivotal under weak conditions often invoked in Wald-type approaches. Three examples show how these can be established using low-level conditions on the quality of the estimated nuisance parameters. Simulation evidence suggests that the Wald approach may undercover more compared to our CFEL approach, especially when the estimating equation is non-linear in the low-dimensional parameter and the first-step estimators have larger finite-sample estimation errors. We illustrate the value of our approach by revisiting the Pennsylvania Reemployment Bonus experiment, which studied the effect of cash bonuses on unemployment duration.