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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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Statistical calibration and exact one-sided simultaneous tolerance intervals for polynomial regression
AU - Han, Yang
AU - Liu, Wei
AU - Bretz, Frank
AU - Wan, Fang
AU - Yang, Ping
N1 - 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
PY - 2016/1
Y1 - 2016/1
N2 - 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.
AB - 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.
KW - Confidence level
KW - Linear regression
KW - Polynomial regression
KW - Quantile line
KW - Simultaneous confidence band
KW - Statistical simulation
KW - Simultaneous tolerance intervals
U2 - 10.1016/j.jspi.2015.07.005
DO - 10.1016/j.jspi.2015.07.005
M3 - Journal article
VL - 168
SP - 90
EP - 96
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
SN - 0378-3758
ER -