Direct semiparametric estimation of single-index models with discrete covariates

Others have developed average derivative estimators of the parameter beta in the model E(Y\X = x) = G(x beta), where G is an unknown function and X is a random vector. These estimators are noniterative and easy to compute but require that X be continuously distributed. This article develops a noniterative, easily computed estimator of beta for models in which some components of X are discrete. The estimator is n(1/2) consistent and asymptotically normal. An application to data on product innovation by German manufacturers illustrates the estimator's usefulness.