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

Lijie Gu, Suojin Wang and Lijian Yang

Computational Statistics & Data Analysis, 2021, vol. 155, issue C

Abstract: 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.

Keywords: Confidence band; Error distribution; Kernel; Local linear; Residuals (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:155:y:2021:i:c:s0167947320301973

DOI: 10.1016/j.csda.2020.107106

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