A method of estimating the average derivative

Banerjee, A.N.

Abstract

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.

Citation

Banerjee, A. (2007). A method of estimating the average derivative. Journal of Econometrics, 136(1), 65-88. https://doi.org/10.1016/j.jeconom.2005.07.010

• Journal Article Type: Article
• Online Publication Date: Aug 24, 2005
• Publication Date: 2007-01
• Deposit Date: Mar 16, 2007
• Journal: Journal of Econometrics
• Print ISSN: 0304-4076
• Electronic ISSN: 1872-6895
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 136
• Issue: 1
• Pages: 65-88
• DOI: https://doi.org/10.1016/j.jeconom.2005.07.010
• Keywords: Semi-parametric estimation, Average derivative estimator, Linear regression.
• Public URL: https://durham-repository.worktribe.com/output/1604438