In this paper, we propose to construct uniform confidence sets 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 pointwise confidence set by explicitly estimating stochastic variations. We extend their ideas and propose a bootstrap approach for constructing uniform confidence sets. We prove that such a bootstrap confidence set is uniform and asymptotically valid. Moreover, our confidence sets are 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 sets.
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