Bootstrapping density-weighted average derivatives

Employing the "small-bandwidth" asymptotic framework of Cattaneo, Crump, and Jansson (2009), this paper studies the properties of several bootstrap-based inference procedures associated with a kernel-based estimator of density-weighted average derivatives proposed by Powell, Stock, and Stoker (1989). In many cases, the validity of bootstrap-based inference procedures is found to depend crucially on whether the bandwidth sequence satisfies a particular (asymptotic linearity) condition. An exception to this rule occurs for inference procedures involving a studentized estimator that employs a "robust" variance estimator derived from the "small-bandwidth" asymptotic framework. The results of a small-scale Monte Carlo experiment are found to be consistent with the theory and indicate in particular that sensitivity with respect to the bandwidth choice can be ameliorated by using the "robust" variance estimator.