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Statistical calibration and exact one-sided simultaneous tolerance intervals for polynomial regression.

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Title: Statistical calibration and exact one-sided simultaneous tolerance intervals for polynomial regression.
Authors: Han, Yang1,2, Liu, Wei1 w.liu@maths.soton.ac.uk, Bretz, Frank3,4, Wan, Fang1, Yang, Ping5
Source: Journal of Statistical Planning & Inference. Jan2016, Vol. 168, p90-96. 7p.
Subjects: Calibration, Simultaneous interpreting, Tolerance intervals (Statistics), Polynomials, Regression analysis
Abstract: Statistical calibration using linear regression is a useful statistical tool having many applications. Calibration for infinitely many future y -values requires the construction of simultaneous tolerance intervals (STI’s). As calibration often involves only two variables x and y and polynomial regression is probably the most frequently used model for relating y with x , construction of STI’s for polynomial regression plays a key role in statistical calibration for infinitely many future y -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. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Statistical Planning & Inference is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
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  Data: Statistical calibration and exact one-sided simultaneous tolerance intervals for polynomial regression.
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  Data: <searchLink fieldCode="AR" term="%22Han%2C+Yang%22">Han, Yang</searchLink><relatesTo>1,2</relatesTo><br /><searchLink fieldCode="AR" term="%22Liu%2C+Wei%22">Liu, Wei</searchLink><relatesTo>1</relatesTo><i> w.liu@maths.soton.ac.uk</i><br /><searchLink fieldCode="AR" term="%22Bretz%2C+Frank%22">Bretz, Frank</searchLink><relatesTo>3,4</relatesTo><br /><searchLink fieldCode="AR" term="%22Wan%2C+Fang%22">Wan, Fang</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Yang%2C+Ping%22">Yang, Ping</searchLink><relatesTo>5</relatesTo>
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  Data: <searchLink fieldCode="DE" term="%22Calibration%22">Calibration</searchLink><br /><searchLink fieldCode="DE" term="%22Simultaneous+interpreting%22">Simultaneous interpreting</searchLink><br /><searchLink fieldCode="DE" term="%22Tolerance+intervals+%28Statistics%29%22">Tolerance intervals (Statistics)</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Regression+analysis%22">Regression analysis</searchLink>
– Name: Abstract
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  Data: Statistical calibration using linear regression is a useful statistical tool having many applications. Calibration for infinitely many future y -values requires the construction of simultaneous tolerance intervals (STI’s). As calibration often involves only two variables x and y and polynomial regression is probably the most frequently used model for relating y with x , construction of STI’s for polynomial regression plays a key role in statistical calibration for infinitely many future y -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. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Statistical Planning & Inference is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.jspi.2015.07.005
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        Text: English
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        PageCount: 7
        StartPage: 90
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      – SubjectFull: Calibration
        Type: general
      – SubjectFull: Simultaneous interpreting
        Type: general
      – SubjectFull: Tolerance intervals (Statistics)
        Type: general
      – SubjectFull: Polynomials
        Type: general
      – SubjectFull: Regression analysis
        Type: general
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      – TitleFull: Statistical calibration and exact one-sided simultaneous tolerance intervals for polynomial regression.
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            NameFull: Liu, Wei
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              Text: Jan2016
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              Y: 2016
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