Generalized jackknife estimators of weighted average derivatives

Matias D. Cattaneo, Richard K. Crump, Michael Jansson

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1243-1256
Number of pages14
JournalJournal of the American Statistical Association
Volume108
Issue number504
DOIs
StatePublished - 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Bias correction
  • Semiparametric estimation
  • Uniform consistency

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