A method of estimating the average derivative

We derive a simple semi-parametric estimator of the “direct” Average Derivative, δ=E(D[m(x)]), where m(x) is the regression function and S, the support of the density of x is compact. We partition S into disjoint bins and the local slope D[m(x)] within these bins is estimated by using ordinary least squares. Our average derivative estimate δ^a, is then obtained by taking the weighted average of these least squares slopes. We show that this estimator is asymptotically normally distributed. We also propose a consistent estimator of the variance of δ^a. Using Monte-Carlo simulation experiments based on a censored regression model (with Tobit Model as a special case) we produce small sample results comparing our estimator with the Härdle-Stoker [1989. Investigating smooth multiple regression by the method of average derivatives. Journal of American Statistical Association 84, 408, 986-995] method. We conclude that δ^a performs better that the Härdle-Stoker estimator for bounded and discontinuous covariates.