How sensitive are average derivatives?

Average derivatives are the mean slopes of regression functions. In practice they are estimated via a nonparametric smoothing technique. Every smoothing method needs a calibration parameter that determines the finite sample performance. In this paper we use the kernel estimation method and develop a formula for the bandwidth that describes the sensitivity of the average derivative estimator. One can determine an optimal smoothing parameter from this formula which tries out to undersmooth the density of the regression variable.