The recent public finance literature often estimates relative excess mass around specific points of the earnings distribution ("kink points" or "notches" of tax schedules, say), and then bootstraps to get standard errors. This is done to nonparametrically estimate local elasticities (responsiveness). I know kernel density is itself problematic for bootstrap, maybe better with subsampling. And this method relates approximations of mass below histograms or empirical distribution functions to local densities. Does the estimator "sound" smooth enough to bootstrap? What rate of convergence is the estimator likely to have (for any method)?
Maybe someone has some intuition. I am not aware of any statistical theory for this problem.