Confidence sets for optimal factor levels of a response surface

Wan, Fang, Liu, Wei, Bretz, Frank and Han, Yang (2016) Confidence sets for optimal factor levels of a response surface. Biometrics, 72 (4), 1285-1293. (doi:10.1111/biom.12500). (PMID:27062462)

Record type: Article

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 - a) 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 - a) 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 - a) confidence level.

Text

wan_bioR2.pdf - Accepted Manuscript

Available under License University of Southampton Accepted Manuscript Licence.

Download (548kB)