title: Confidence sets for optimal factor levels of a response surface.
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 (1-α) 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 (1-α) 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 (1-α) confidence level.
authors.affiliation: Lancaster University, Bailrigg, Lancaster LA1 4YW, U.K.
authors.forename: Fang
authors.initials: F
authors.lastname: Wan
authors.affiliation: University of Southampton, University Rd, Southampton SO17 1BJ, U.K.
authors.forename: Wei
authors.initials: W
authors.lastname: Liu
authors.affiliation: Novartis Pharma AG, Novartis Campus, Basel CH-4002, Switzerland.
authors.forename: Frank
authors.initials: F
authors.lastname: Bretz
authors.affiliation: University of Exeter, Exeter, Devon EX4, U.K.
authors.forename: Yang
authors.initials: Y
authors.lastname: Han
mesh_terms: D001699:Biometry / Q000379:methods; D003198:Computer Simulation; D016001:Confidence Intervals; D006801:Humans; D015233:Models, Statistical; D012044:Regression Analysis
keywords: Parametric regression; Response surface; Semiparametric regression; Statistical inference; Statistical simulation