A method of estimating the average derivative
提出一种简单的半参数估计量来估计平均导数，通过将自变量支撑划分为不相交的区间并用普通最小二乘法估计局部斜率，再取加权平均。该估计量渐近正态，方差可一致估计。蒙特卡洛模拟表明，对于有界或不连续的协变量，该估计量优于Härdle-Stoker方法。
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 , 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 . 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 performs better that the Härdle–Stoker estimator for bounded and discontinuous covariates.