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Abstract:
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In this talk, 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.
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