Generalized Jackknife Estimators of Weighted Average Derivatives

Abstract

Asymptotic linearity of kernel-based weighted average derivative estimators is established under weak conditions. The bandwidth conditions employed are shown to be necessary in some cases. A bias-corrected version of the estimator is proposed and shown to be asymptotically linear under yet weaker bandwidth conditions. Consistency of an analog estimator of the asymptotic variance is established. To establish the results, a novel result on uniform convergence rates for kernel estimators is obtained.