Rights statement: This is the peer reviewed version of the following article: Wan, F., Liu, W., Bretz, F. and Han, Y. (2016), Confidence sets for optimal factor levels of a response surface. Biom, 72: 1285–1293. doi:10.1111/biom.12500 which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1111/biom.12500/abstract This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.
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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Confidence sets for optimal factor levels of a response surface
AU - Wan, Fang
AU - Liu, Wei
AU - Bretz, Frank
AU - Han, Yang
N1 - This is the peer reviewed version of the following article:Wan, F., Liu, W., Bretz, F. and Han, Y. (2016), Confidence sets for optimal factor levels of a response surface. Biom, 72: 1285–1293. doi:10.1111/biom.12500 which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1111/biom.12500/abstract This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.
PY - 2016/12
Y1 - 2016/12
N2 - Construction of confidence sets for the optimal factor levels is an important topic in response surfaces methodology. In Wan et al. (2015), an exact inline image 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 inline image 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 inline image confidence level.
AB - Construction of confidence sets for the optimal factor levels is an important topic in response surfaces methodology. In Wan et al. (2015), an exact inline image 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 inline image 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 inline image confidence level.
KW - Parametric regression
KW - Response surface
KW - Semiparametric regression
KW - Statistical inference
KW - Statistical simulation
U2 - 10.1111/biom.12500
DO - 10.1111/biom.12500
M3 - Journal article
VL - 72
SP - 1285
EP - 1293
JO - Biometrics
JF - Biometrics
SN - 0006-341X
IS - 4
ER -