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In this paper, we propose to construct confidence bands by bootstrapping thedebiased kernel density estimator (for density estimation) and the debiasedlocal polynomial regression estimator (for regression analysis). The idea ofusing a debiased estimator was recently employed by Calonico et al. (2018b) toconstruct a confidence interval of the density function (and regressionfunction) at a given point by explicitly estimating stochastic variations. Weextend their ideas of using the debiased estimator and further propose abootstrap approach for constructing simultaneous confidence bands. Thismodified method has an advantage that we can easily choose the smoothingbandwidth from conventional bandwidth selectors and the confidence band will beasymptotically valid. We prove the validity of the bootstrap confidence bandand generalize it to density level sets and inverse regression problems.Simulation studies confirm the validity of the proposed confidence bands/sets.We apply our approach to an Astronomy dataset to show its applicability

Nonparametric Inference via Bootstrapping the Debiased Estimator