NONPARAMETRIC AND SEMIPARAMETRIC ESTIMATION WITH DISCRETE REGRESSORS

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.