Generalized Jackknife Estimators of Weighted Average Derivatives

• Activity Number: 157
• Type: Invited
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: JASA, Theory and Methods
• Author(s): Matias Damian Cattaneo*+ and Richard Crump and Michael Jansson
• Companies: University of Michigan and Federal Reserve Bank of New York and University of California at Berkeley
• Keywords: Semiparametric estimation ; bias correction ; uniform consistency

Abstract

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. 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 paper includes details on the theoretical proofs and other analytic derivations, and further results from the simulation study.