# Nonparametric Inference via Bootstrapping the Debiased Estimator

arXiv: https://arxiv.org/abs/1702.07027 · HTML: https://mlsanity.com/paper/1702.07027/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2017.

## Built on by (most cited first, 1 of 1)

- [Uncertainty quantification for distributed regression](https://mlsanity.com/paper/2105.11425/) (2021)

## Abstract (arXiv)

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 recently employed by Calonico et al. (2018b) to construct a confidence interval of the density function (and regression function) at a given point by explicitly estimating stochastic variations. We extend their ideas of using the debiased estimator and further propose a bootstrap approach for constructing simultaneous confidence bands. This modified method has an advantage that we can easily choose the smoothing bandwidth from conventional bandwidth selectors and the confidence band will be asymptotically valid. We prove the validity of the bootstrap confidence band and 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