Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 829-836 |
| Number of pages | 8 |
| Journal | European Journal of Operational Research |
| Volume | 252 |
| Issue number | 3 |
| DOIs | |
| State | Published - Aug 1 2016 |
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All Science Journal Classification (ASJC) codes
- Computer Science(all)
- Modeling and Simulation
- Management Science and Operations Research
- Information Systems and Management
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A confidence region for the ridge path in multiple response surface optimization. / Shi, Liangxing; Lin, Dennis K.J.; Peterson, John J.
In: European Journal of Operational Research, Vol. 252, No. 3, 01.08.2016, p. 829-836.Research output: Contribution to journal › Article
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.
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.
UR - http://www.scopus.com/inward/record.url?scp=84960810580&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84960810580&partnerID=8YFLogxK
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 -