Estimation of Semiparametric Models when the Criterion Function Is Not Smooth
给出半参数优化估计量一致性和渐近正态性的易验证充分条件，适用于准则函数不光滑且依赖参数相关非参数估计的情形，并证明自助法可构造正确渐近置信域，通过命中率和部分线性中位数回归两个例子展示应用。
We provide easy to verify sufficient conditions for the consistency and asymptotic normality of a class of semiparametric optimization estimators where the criterion function does not obey standard smoothness conditions and simultaneously depends on some nonparametric estimators that can themselves depend on the parameters to be estimated. Our results extend existing theories such as those of Pakes and Pollard (1989), Andrews (1994a), and Newey (1994). We also show that bootstrap provides asymptotically correct confidence regions for the finite dimensional parameters. We apply our results to two examples: a 'hit rate' and a partially linear median regression with some endogenous regressors.