Generalized Jackknife Estimators of Weighted Average Derivatives

• 成果类型: Article
• 署名作者: Cattaneo, Matias D.; Crump, Richard K.; Jansson, Michael
• 署名单位: University of Michigan System; University of Michigan; Federal Reserve System - USA; Federal Reserve Bank - New York; University of California System; University of California Berkeley
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2012.745810
• 发表日期: 2013
• 页码: 1243-1256
• 关键词: kernel estimation; semiparametric estimation; index models; coefficients; regression; variance

摘要

With the aim of improving the quality of asymptotic distributional approximations for nonlinear functionals of nonparametric estimators, this article revisits the large-sample properties of an importantmember 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. Implementational details of the estimators are discussed, including bandwidth selection procedures. Consistency of an analog estimator of the asymptotic variance is also established. Numerical results from a simulation study and an empirical illustration are reported. To establish the results, a novel result on uniform convergence rates for kernel estimators is obtained. The online supplemental material to this article includes details on the theoretical proofs and other analytic derivations, and further results from the simulation study.