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    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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Confidence sets for optimal factor levels of a response surface

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Confidence sets for optimal factor levels of a response surface. / Wan, Fang; Liu, Wei; Bretz, Frank; Han, Yang.

In: Biometrics, Vol. 72, No. 4, 12.2016, p. 1285-1293.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Wan, F, Liu, W, Bretz, F & Han, Y 2016, 'Confidence sets for optimal factor levels of a response surface', Biometrics, vol. 72, no. 4, pp. 1285-1293. https://doi.org/10.1111/biom.12500

APA

Wan, F., Liu, W., Bretz, F., & Han, Y. (2016). Confidence sets for optimal factor levels of a response surface. Biometrics, 72(4), 1285-1293. https://doi.org/10.1111/biom.12500

Vancouver

Author

Wan, Fang ; Liu, Wei ; Bretz, Frank ; Han, Yang. / Confidence sets for optimal factor levels of a response surface. In: Biometrics. 2016 ; Vol. 72, No. 4. pp. 1285-1293.

Bibtex

@article{dffb9050a457424ab4f6ee1c5dcf6ba7,
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 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.",
keywords = "Parametric regression, Response surface, Semiparametric regression, Statistical inference, Statistical simulation",
author = "Fang Wan and Wei Liu and Frank Bretz and Yang Han",
note = "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.",
year = "2016",
month = dec,
doi = "10.1111/biom.12500",
language = "English",
volume = "72",
pages = "1285--1293",
journal = "Biometrics",
issn = "0006-341X",
publisher = "Wiley-Blackwell",
number = "4",

}

RIS

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 -