Premium
Confidence bands for smoothness in nonparametric regression
Author(s) -
Faraway Julian
Publication year - 2016
Publication title -
stat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.61
H-Index - 18
ISSN - 2049-1573
DOI - 10.1002/sta4.100
Subject(s) - nonparametric statistics , smoothness , nonparametric regression , confidence and prediction bands , smoothing , inference , confidence interval , econometrics , regression , statistics , computer science , mathematics , artificial intelligence , mathematical analysis
The choice of the smoothing parameter in nonparametric regression is critical to the form of the estimated curve and any inference that follows. Many methods are available that will generate a single choice for this parameter. Here, we argue that the considerable uncertainty in this choice should be explicitly represented. The construction of standard simultaneous confidence bands in nonparametric regression often requires difficult mathematical arguments. We question their practical utility, presenting several deficiencies. We propose a new kind of confidence band that reflects the uncertainty regarding the smoothness of the estimate. Copyright © 2016 John Wiley & Sons, Ltd.