Title: Nonparametric Inference via Bootstrapping the Debiased Estimator,
Abstract: In this paper, we propose to construct confidence bands by bootstrapping the
debiased kernel density estimator (for density estimation) and the debiased
local polynomial regression estimator (for regression analysis). The idea of
using a debiased estimator was first introduced in Calonico et al. (2015),
where they construct a confidence interval of the density function (and
regression function) at a given point by explicitly estimating stochastic
variations. We extend their ideas and propose a bootstrap approach for
constructing confidence bands that is uniform for every point in the support.
We prove that the resulting bootstrap confidence band is asymptotically valid
and is compatible with most tuning parameter selection approaches, such as the
rule of thumb and cross-validation. We further generalize our method to
confidence sets of density level sets and inverse regression problems.
Simulation studies confirm the validity of the proposed confidence bands/sets.