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Confidence sets for optimal factor levels of a response surface
Author(s) -
Wan Fang,
Liu Wei,
Bretz Frank,
Han Yang
Publication year - 2016
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.12500
Subject(s) - confidence interval , confidence region , confidence distribution , cdf based nonparametric confidence interval , quadratic function , mathematics , robust confidence intervals , parametric statistics , confidence and prediction bands , function (biology) , quadratic equation , univariate , set (abstract data type) , statistics , computer science , multivariate statistics , geometry , evolutionary biology , biology , programming language
Summary 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.