Statistical calibration and exact one-sided simultaneous tolerance intervals for polynomial regression
Statistical calibration and exact one-sided simultaneous tolerance intervals for polynomial regression
Statistical calibration using linear regression is a useful statistical tool having many applications. Calibration for infinitely many future yy-values requires the construction of simultaneous tolerance intervals (STI’s). As calibration often involves only two variables xx and yy and polynomial regression is probably the most frequently used model for relating yy with xx, construction of STI’s for polynomial regression plays a key role in statistical calibration for infinitely many future yy-values. The only exact STI’s published in the statistical literature are provided by Mee et al. (1991) and Odeh and Mee (1990). But they are for a multiple linear regression model, in which the covariates are assumed to have no functional relationships. When applied to polynomial regression, the resultant STI’s are conservative. In this paper, one-sided exact STI’s have been constructed for a polynomial regression model over any given interval. The available computer program allows the exact methods developed in this paper to be implemented easily. Real examples are given for illustration.
confidence level, linear regression, polynomial regression, quantile line, simultaneous confidence band, simultaneous tolerance intervals, statistical simulation
90-96
Han, Yang
f5a6d423-6a9c-487c-be8d-17dcdc35829f
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Bretz, Frank
aa8a675f-f53f-4c50-8931-8e9b7febd9f0
Wan, Fang
dd06c26a-977d-41fd-9d8c-58c7393d90c2
Yang, Ping
3dba2634-eb2b-4df8-a995-1061b841afe1
January 2016
Han, Yang
f5a6d423-6a9c-487c-be8d-17dcdc35829f
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Bretz, Frank
aa8a675f-f53f-4c50-8931-8e9b7febd9f0
Wan, Fang
dd06c26a-977d-41fd-9d8c-58c7393d90c2
Yang, Ping
3dba2634-eb2b-4df8-a995-1061b841afe1
Han, Yang, Liu, Wei, Bretz, Frank, Wan, Fang and Yang, Ping
(2016)
Statistical calibration and exact one-sided simultaneous tolerance intervals for polynomial regression.
Journal of Statistical Planning and Inference, 168, .
(doi:10.1016/j.jspi.2015.07.005).
Abstract
Statistical calibration using linear regression is a useful statistical tool having many applications. Calibration for infinitely many future yy-values requires the construction of simultaneous tolerance intervals (STI’s). As calibration often involves only two variables xx and yy and polynomial regression is probably the most frequently used model for relating yy with xx, construction of STI’s for polynomial regression plays a key role in statistical calibration for infinitely many future yy-values. The only exact STI’s published in the statistical literature are provided by Mee et al. (1991) and Odeh and Mee (1990). But they are for a multiple linear regression model, in which the covariates are assumed to have no functional relationships. When applied to polynomial regression, the resultant STI’s are conservative. In this paper, one-sided exact STI’s have been constructed for a polynomial regression model over any given interval. The available computer program allows the exact methods developed in this paper to be implemented easily. Real examples are given for illustration.
Text
Han_Statistical.pdf
- Accepted Manuscript
More information
Accepted/In Press date: 21 July 2015
e-pub ahead of print date: 29 July 2015
Published date: January 2016
Keywords:
confidence level, linear regression, polynomial regression, quantile line, simultaneous confidence band, simultaneous tolerance intervals, statistical simulation
Organisations:
Mathematical Sciences, Statistical Sciences Research Institute
Identifiers
Local EPrints ID: 382773
URI: http://eprints.soton.ac.uk/id/eprint/382773
ISSN: 0378-3758
PURE UUID: 0fff78b2-f3d6-4ef8-9bc3-d1c575d57b27
Catalogue record
Date deposited: 21 Oct 2015 13:30
Last modified: 15 Mar 2024 02:43
Export record
Altmetrics
Contributors
Author:
Yang Han
Author:
Frank Bretz
Author:
Fang Wan
Author:
Ping Yang
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
