TY - JOUR
T1 - A confidence region for the ridge path in multiple response surface optimization
AU - Shi, Liangxing
AU - Lin, Dennis K.J.
AU - Peterson, John J.
N1 - Funding Information:
This research was supported by National Natural Science Foundation of China (Project No. 71102140 ), National Science Foundation for Distinguished Young Scholars of China (Project No. 71225006) and National Security Agent via Grant H98230-15-1-0253. We are grateful to the editor and referees, whose sharply focused comments were extremely helpful.
Publisher Copyright:
© 2016 Elsevier B.V. All rights reserved.
PY - 2016/8/1
Y1 - 2016/8/1
N2 - Ridge analysis allows the analyst to explore the optimal operating conditions of the experimental factors. A confidence region is desirable for the estimated ridge path. Most literature concentrates on the univariate response situation. Little is known for the confidence region of the ridge path for the multivariate response; only a large-sample confidence interval for the ridge path is available. The simultaneous coverage rate for the existing interval is typically too conservative in practice, especially for small sample sizes. In this paper, the ridge path (via desirability function) is estimated based on the seemingly unrelated regression (SUR) model as well as standard multivariate regression (SMR) model, and a conservative confidence interval suitable for small sample sizes is proposed. It is shown that the proposed method outperforms the existing methods. Real-life examples and simulative study are given for illustration.
AB - Ridge analysis allows the analyst to explore the optimal operating conditions of the experimental factors. A confidence region is desirable for the estimated ridge path. Most literature concentrates on the univariate response situation. Little is known for the confidence region of the ridge path for the multivariate response; only a large-sample confidence interval for the ridge path is available. The simultaneous coverage rate for the existing interval is typically too conservative in practice, especially for small sample sizes. In this paper, the ridge path (via desirability function) is estimated based on the seemingly unrelated regression (SUR) model as well as standard multivariate regression (SMR) model, and a conservative confidence interval suitable for small sample sizes is proposed. It is shown that the proposed method outperforms the existing methods. Real-life examples and simulative study are given for illustration.
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U2 - 10.1016/j.ejor.2016.01.037
DO - 10.1016/j.ejor.2016.01.037
M3 - Article
AN - SCOPUS:84960810580
VL - 252
SP - 829
EP - 836
JO - European Journal of Operational Research
JF - European Journal of Operational Research
SN - 0377-2217
IS - 3
ER -