SEMIPARAMETRIC ESTIMATION WITH GENERATED COVARIATES
研究了一类半参数估计量，其中无穷维扰动参数包含用生成协变量非参数估计的条件期望函数，给出了估计量根号n一致和渐近正态的条件，推导了渐近方差公式并验证了自助法的有效性。
We study a general class of semiparametric estimators when the infinite-dimensional nuisance parameters include a conditional expectation function that has been estimated nonparametrically using generated covariates. Such estimators are used frequently to e.g., estimate nonlinear models with endogenous covariates when identification is achieved using control variable techniques. We study the asymptotic properties of estimators in this class, which is a nonstandard problem due to the presence of generated covariates. We give conditions under which estimators are root- n consistent and asymptotically normal, derive a general formula for the asymptotic variance, and show how to establish validity of the bootstrap.