Bootstrap of residual processes in regression: to smooth or not to smooth?

• 成果类型: Article
• 署名作者: Neumeyer, N.; van Keilegom, I.
• 署名单位: University of Hamburg; KU Leuven
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asz009
• 发表日期: 2019
• 页码: 385400
• 关键词: of-fit tests; Nonparametric Regression; error distribution; confidence bands; approximations; distributions; models

摘要

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.