Gradient-based bandwidth selection for estimating average derivatives

•We propose a new average derivative estimator based on pointwise derivative estimate.•Our estimator reaches the optimal convergence rate.•The superiority of our proposed estimator is illustrated by simulation.

In this paper, we propose to estimate average derivatives of a function by averaging the sample pointwise local linear derivatives with the bandwidth being selected optimally. Our estimator has better finite sample performance than that of Li, Lu & Ullah (2003) because our pointwise derivative estimate reaches the optimal convergence rate. Simulations confirm our theoretical analysis.