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

Yang Han, Wei Liu, Frank Bretz, Fang Wan, Ping Yang

    Research output: Contribution to journalArticlepeer-review


    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.

    Original languageEnglish
    Pages (from-to)90-96
    JournalJournal of Statistical Planning and Inference
    Early online date29 Jul 2015
    Publication statusPublished - Jan 2016


    • Confidence level
    • Linear regression
    • Polynomial regression
    • Quantile line
    • Simultaneous confidence band
    • Simultaneous tolerance intervals
    • Statistical simulation


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