Comment Donglin Zeng

Cattaneo, Grump, and Jansson (2013) present an interesting estimator, namely the generalized jackknife estimator, for estimating weighted average derivatives. Starting with a high-order (in this case, second-order) linearization of the estimating equation, they obtain the asymptotic approximation under a weak bandwidth selection which does not require the standard convergence rate of the nonparametric estimator faster than n1/4. Specifically, an asymptotic approximation of θ̂n(Hn) is given when n|Hn|λmin(Hn)/ log(n)3/2 → ∞. The polynomial expression of the asymptotic bias in θ̂n(Hn) in terms of Hn further motivates the construction of the generalized jackknife estimator θ̃n(Hn, c), which eliminates the asymptotic bias. They present a number of simulation studies demonstrating that θ̃n(Hn, c) leads to noticeable bias reduction with small bandwidths. Another contribution includes a proof of the uniform convergence of the kernel estimators.