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    Rights statement: This is the author’s version of a work that was accepted for publication in Journal of Statistical Planning and Inference. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Statistical Planning and Inference, 168, 2016 DOI: 10.1016/j.jspi.2015.07.005

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

Research output: Contribution to journalJournal articlepeer-review

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  • Yang Han
  • Wei Liu
  • Frank Bretz
  • Fang Wan
  • Ping Yang
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<mark>Journal publication date</mark>01/2016
<mark>Journal</mark>Journal of Statistical Planning and Inference
Volume168
Number of pages7
Pages (from-to)90-96
Publication StatusPublished
Early online date29/07/15
<mark>Original language</mark>English

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.

Bibliographic note

This is the author’s version of a work that was accepted for publication in Journal of Statistical Planning and Inference. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Statistical Planning and Inference, 168, 2016 DOI: 10.1016/j.jspi.2015.07.005