Smooth simultaneous confidence band for the error distribution function in nonparametric regression

A smooth simultaneous confidence band (SCB) is constructed for the distribution of unobserved errors in a nonparametric regression model based on a plug-in kernel distribution estimator. The normalized estimation error process is shown to converge to a Gaussian process. Simulation experiments indica...

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Bibliographic Details
Published in:Computational statistics & data analysis 2021-03, Vol.155, p.107106, Article 107106
Main Authors: Gu, Lijie, Wang, Suojin, Yang, Lijian
Format: Article
Language:English
Subjects:
Confidence band
Error distribution
Kernel
Local linear
Residuals
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Summary:A smooth simultaneous confidence band (SCB) is constructed for the distribution of unobserved errors in a nonparametric regression model based on a plug-in kernel distribution estimator. The normalized estimation error process is shown to converge to a Gaussian process. Simulation experiments indicate that the proposed SCB not only strikes an intelligent balance between coverage probability and precision, but also achieves surprisingly as much as double efficiency of the classical infeasible SCB. Furthermore, extensive empirical studies are carried out to compare the proposed method with the smooth residual bootstrap method in order to demonstrate the usefulness of each of these methods. As an illustration, the proposed SCB is applied to the Old Faithful geyser data for testing the error distribution.
ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2020.107106