Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 13, Number 1 (2019), 2194-2256.
Nonparametric inference via bootstrapping the debiased estimator
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.
Electron. J. Statist., Volume 13, Number 1 (2019), 2194-2256.
Received: June 2018
First available in Project Euclid: 28 June 2019
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Cheng, Gang; Chen, Yen-Chi. Nonparametric inference via bootstrapping the debiased estimator. Electron. J. Statist. 13 (2019), no. 1, 2194--2256. doi:10.1214/19-EJS1575. https://projecteuclid.org/euclid.ejs/1561687408