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- Title
Bootstrap of residual processes in regression: to smooth or not to smooth?
- Authors
Neumeyer, N; Keilegom, I Van
- Abstract
In this paper we consider regression models with centred errors, independent of the covariates. Given independent and identically distributed data and given an estimator of the regression function, which can be parametric or nonparametric in nature, we estimate the distribution of the error term by the empirical distribution of estimated residuals. To approximate the distribution of this estimator, Koul & Lahiri (1994) and Neumeyer (2009) proposed bootstrap procedures based on smoothing the residuals before drawing bootstrap samples. So far it has been an open question as to whether a classical nonsmooth residual bootstrap is asymptotically valid in this context. Here we solve this open problem and show that the nonsmooth residual bootstrap is consistent. We illustrate the theoretical result by means of simulations, which demonstrate the accuracy of this bootstrap procedure for various models, testing procedures and sample sizes.
- Subjects
STATISTICAL bootstrapping; REGRESSION analysis; OPEN-ended questions; DISTRIBUTION (Probability theory)
- Publication
Biometrika, 2019, Vol 106, Issue 2, p385
- ISSN
0006-3444
- Publication type
Article
- DOI
10.1093/biomet/asz009