Gradient Based Smoothing Parameter Selection for Nonparametric Regression Estimation*

Data-driven bandwidth selection based on the gradient of an unknown regression function is considered. Uncovering gradients nonparametrically is of crucial importance across a broad range of economic environments such as determining risk premium or recovering distributions of individual preferences. The procedure developed here is shown to deliver bandwidths which have the optimal rate of convergence for the estimation of gradients. We provide a detailed theoretical account of this new approach to smoothing parameter selection. An important additional advantage of our proposed method over the conventional cross-validation bandwidth selection method is that our approach overcomes the tendency of traditional data-driven approaches to engage in under smoothing. Both simulated and (several) empirical examples showcase the finite sample attraction of this new mechanism. 1. Overview Nonparametric estimation and inferential approaches in applied econometric work are now commonplace. The allure of these methods are that they allow users to mitigate the influence that a specific parametric model places on the analysis and can provide deeper insights into the phenomena of interest relative to their rigid parametric counterparts. Moreover, for conducting policy analysis, the use of nonparametric methods is buttressed by the fact that policy conclusions should hinge on distribution-free methods when knowledge of the true relationship is vacuous (McAfee & Vincent 1992). A key component of any nonparametric (or semiparametric) analysis is the selection of the smoothing (bandwidth) parameter(s) which dictates the behavior of the resulting estimates/inferences. In this paper we develop a novel approach to conduct data-driven bandwidth selection. The motivation for our approach stems from the fact that in applied econometric milieus interest typically hinges on the gradients of the regression function, i.e., marginal effects, rather than the regression State University of New York at Binghamton, Texas A&M University, University of Miami Date: March 28, 2011.