Nonparametric and Semiparametric Estimation with Discrete Regressors
讨论回归模型中解释变量为离散时的非参数与半参数推断方法。当离散变量有有限支撑时，对相同变量值的因变量取平均可得根号n一致的期望估计；并证明即使支撑无限，该权重序列也满足Stone(1977)的一致性。结果应用于半参数模型估计。
This note is concerned with nonparametric and semiparametric inference in regression models where regressors are not continuous. When regressors are discrete with finite support, a mere average of those observations of the dependent variable with the same regressor value will yield a root-n-consistent conditional expectation estimate. We show that sequences of weights constructed in this way are consistent in the sense of Stone (1977), even when the discrete regressors have infinite support. The results are applied to the estimation of semiparametric models.