Confidence Sets for Optimal Factor Levels of a Response Surface

Fang Wan, Wei Liu, Frank Bretz, Yang Han

    Research output: Contribution to journalArticlepeer-review

    Abstract

    Construction of confidence sets for the optimal factor levels is an important topic in response surfaces methodology. In Wan et al. (2015), an exact math formula confidence set has been provided for a maximum or minimum point (i.e., an optimal factor level) of a univariate polynomial function in a given interval. In this article, the method has been extended to construct an exact math formula confidence set for the optimal factor levels of response surfaces. The construction method is readily applied to many parametric and semiparametric regression models involving a quadratic function. A conservative confidence set has been provided as an intermediate step in the construction of the exact confidence set. Two examples are given to illustrate the application of the confidence sets. The comparison between confidence sets indicates that our exact confidence set is better than the only other confidence set available in the statistical literature that guarantees the math formula confidence level.
    Original languageEnglish
    Pages (from-to)1285-1293
    JournalBiometrics
    Volume72
    Issue number4
    Early online date8 Apr 2016
    DOIs
    Publication statusPublished - Dec 2016

    Keywords

    • Parametric regression
    • Response surface
    • Semiparametric regression
    • Statistical inference
    • Statistical simulation

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