Generalized Jackknife Estimators of Weighted Average Derivatives-加权平均导数的广义折刀估计量

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英文文献：Generalized Jackknife Estimators of Weighted Average Derivatives-加权平均导数的广义折刀估计量
英文文献作者：Matias D. Cattaneo,Richard K. Crump,Michael Jansson
英文文献摘要：
With the aim of improving the quality of asymptotic distributional approximations for nonlinear functionals of nonparametric estimators, this paper revisits the large-sample properties of an important member of that class, namely a kernel-based weighted average derivative estimator. Asymptotic linearity of the estimator is established under weak conditions. Indeed, we show that the bandwidth conditions employed are 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 also established. To establish the results, a novel result on uniform convergence rates for kernel estimators is obtained.

摘要为了提高非线性泛函非参数估计量的渐近分布逼近的性质，本文重新考察了该类中一个重要成员的大样本性质，即基于核的加权平均导数估计量。在弱条件下，建立了估计量的渐近线性。事实上，我们证明了所采用的带宽条件在某些情况下是必要的。在较弱带宽条件下，该估计量的偏置修正版本被证明是渐近线性的。并建立了渐近方差模拟估计量的相合性。为了证明这些结果，得到了核估计量一致收敛率的一个新的结果。

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