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.