HOW SENSITIVE ARE AVERAGE DERIVATIVES

Average derivatives are the mean slopes of regression functions. In pr actice they are estimated via a nonparametric smoothing technique. Eve ry 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 sens itivity of the average derivative estimator. One can determine an opti mal smoothing parameter from this formula which tries out to undersmoo th the density of the regression variable.