Gradient Based Smoothing Parameter Selection for Nonparametric Regression Estimation

Uncovering gradients is of crucial importance across a broad range of economic environments. Here we consider data-driven bandwidth selection based on the gradient of an unknown regression function. The procedure developed here is automatic and does not require initial estimation of unknown functions with pilot bandwidths. We prove that it delivers bandwidths which have the optimal rate of convergence for the gradient. Both simulated and empirical examples showcase the finite sample attraction of this new mechanism.