Optimal Designs for Multi-Response Nonlinear Regression Models With Several Factors via Semidefinite Programming

References

• Atashgah, A. B., and Seifi, A. (2007), “Application of Semi-Definite Programming to the Design of Multi-Response Experiments,” IIE Transactions, 39, 763–769.
   Web of Science ®Google Scholar
• ——— (2009), “Optimal Design of Multi-Response Experiments Using Semi-Definite Programming,” Optimization and Engineering, 10, 75–90.
   Web of Science ®Google Scholar
• Berger, M. P. F., and Wong, W. K. (2009), An Introduction to Optimal Designs for Social and Biomedical Research, Chichester, UK: Wiley.
   Google Scholar
• Bischoff, W. (1993), “On D-Optimal Designs for Linear Models Under Correlated Observations With an Application to a Linear Model With Multiple Response,” Journal of Statistical Planning and Inference, 37, 69–80.
   Web of Science ®Google Scholar
• ——— (1995), “Determinant Formulas With Applications to Designing When the Observations are Correlated,” Annals of the Institute of Statistical Mathematics, 47, 385–399.
   Web of Science ®Google Scholar
• Bose, M., and Mukerjee, R. (2015), “Optimal Design Measures Under Asymmetric Errors, With Application to Binary Design Points,” Journal of Statistical Planning and Inference, 159, 28–36.
   Web of Science ®Google Scholar
• Boyd, S., and Vandenberghe, L. (2004), Convex Optimization, New York: Cambridge University Press.
   Google Scholar
• Chang, F. C., Huang, M. N. L., Lin, D. K. J., and Yang, H. C. (2001), “Optimal Designs for Dual Response Polynomial Regression Models,” Journal of Statistical Planning and Inference, 93, 309–322.
   Web of Science ®Google Scholar
• Chang, S. (1997), “An Algorithm to Generate Near D-Optimal Designs for Multiple Response Surface Models,” IIE Transactions, 29, 1073–1081.
   Web of Science ®Google Scholar
• Dean, A., Morris, M., Stufken, J., and Bingham, D. (2015), Handbook of Design and Analysis of Experiments, New York: CRC Press.
   Google Scholar
• Dette, H., Hoyden, L., Kuhnt, S., and Schorning, K. (2013), “Optimal Designs for Multi-Response Generalized Linear Models With Applications in Thermal Spraying,” available at http://arxiv.org/pdf/1312.4472.pdf
   Google Scholar
• Dragalin, V., Fedorov, V. V., and Wu, Y. (2008), “Two-Stage Design for Dose-Finding That Accounts for Both Efficacy and Safety,” Statistics in Medicine, 27, 5156–5176.
   PubMed Web of Science ®Google Scholar
• Duarte, B. P. M., and Wong, W. K. (2015), “Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach,” International Statistical Review, 83, 239–262.
   PubMed Web of Science ®Google Scholar
• Duarte, B. P. M., Wong, W. K., and Oliveira, N. M. C. (2016), “Model-Based Optimal Design of Experiments - Semidefinite and Nonlinear Programming Formulations,” Chemometrics and Intelligent Laboratory Systems, 151, 153–163.
   PubMed Web of Science ®Google Scholar
• Duarte, B. P. M., Sagnol, G., and Wong, W. K. (2018), “An Algorithm Based on Semidefinite Programming for Finding Minimax Optimal Designs,” Computational Statistics and Data Analysis, 119, 99–117.
   Web of Science ®Google Scholar
• Fedorov, V., Gagnon, R., and Leonov, S. (2001), “Optimal Design for Multiple Responses With Variance Depending on Unknown Parameters,” GSK BDS Technical Report No. 2001 – 03, GlaxoSmithKline Pharmaceuticals.
   Google Scholar
• Fedorov, V. V. (1972), Theory of Optimal Experiments, New York: Academic Press.
   Google Scholar
• Fedorov, V. V., and Wu, Y. (2007), “Dose Finding Designs for Continuous Responses and Binary Utility,” Journal of Biopharmaceutical Statistics, 17, 1085–1096.
   PubMed Web of Science ®Google Scholar
• Fedorov, V. V., Wu, Y., and Zhang, R. (2012), “Optimal Dose-Finding Designs With Correlated Continuous and Discrete Responses,” Statistics in Medicine, 31, 217–234.
   PubMed Web of Science ®Google Scholar
• Grant, M. C., and Boyd, S. P. (2013), The CVX Users’ Guide, Release 2.0 (beta), Standford University, CVX Research, Inc., available at http://cvxr.com/cvx/doc/CVX.pdf
   Google Scholar
• Gueorguieva, I., Aarons, L., Ogungbenro, K., Jorga, K. M., Rodgers, T., and Rowland, M. (2006), “Optimal Design for Multivariate Response Pharmacokinetic Models,” Journal of Pharmacokinetics and Pharmacodynamics, 33, 97–124.
   PubMed Web of Science ®Google Scholar
• Heise, M. A., and Myers, R. M. (1996), “Optimal Designs for Bivariate Logistic Regression,” Biometrics, 52, 613–624.
   Web of Science ®Google Scholar
• Horn, R. A., and Johnson, C. R. (2009), Matrix Analysis, New York: Cambridge University Press.
   Google Scholar
• Huang, M. L., Chen, R. B., Lin, C. S., and Wong, W. K. (2006), “Optimal Designs for Parallel Models With Correlated Responses,” Statistica Sinica, 16, 121–133.
   Web of Science ®Google Scholar
• Imhof, L. (2000), “Optimum Designs for a Multiresponse Regression Model,” Journal of Multivariate Analysis, 72, 120–131.
   Web of Science ®Google Scholar
• Kim, S. (2014), Optimal Experimental Design Under a New Multivariate Weibull Regression Function, Ph.D. dissertation, Department of Statistics, University of Missouri, MO.
   Google Scholar
• Kpamegan, E. P. (1998), “D-Optimal Designs Given a Bivariate Probit Response Function,” in New Developments and Applications in Experimental Design, eds, N. Flournoy, W. F. Rosenberger, and W. K. Wong, Hayward, California: Institute of Mathematical Statistics, pp. 62–72.
   Google Scholar
• Krafft, O., and Schaefer, M. (1992), “D-Optimal Designs for a Multivariate Regression Model,” Journal of Multivariate Analysis, 42, 130–140.
   Web of Science ®Google Scholar
• Liu, X., Yue, R. X., and Hickernell, F. J. (2011), “Optimality Criteria for Multiresponse Linear Models Based on Predictive Ellipsoids,” Statistica Sinica, 21, 421–432.
   Web of Science ®Google Scholar
• Magnusdottir, B. T. (2013), “C-Optimal Designs for the Bivariate Emax Model,” in mODa 10-Advances in Model-Oriented Design and Analysis, eds. D. Uciński, A. C. Atkinson, and M. Patan, Switzerland: Springer, pp. 153–161.
   Google Scholar
• Montgomery, D. C. (2013), Design and Analysis of Experiments (8th ed.), New York: Wiley.
   Google Scholar
• Mukhopadhyay, S., and Khuri, A. I. (2008), “Comparison of Designs for Multivariate Generalized Linear Models,” Journal of Statistical Planning and Inference, 138, 169–183.
   Web of Science ®Google Scholar
• Papp, D. (2012), “Optimal Designs for Rational Function Regression,” Journal of the American Statistical Association, 107, 400–411.
   Web of Science ®Google Scholar
• Pukelsheim, F. (1993), Optimal Design of Experiments, New York: Wiley.
   Google Scholar
• Sagnol, G. (2011), “Computing Optimal Designs of Multiresponse Experiments Reduces to Second-Order Cone Programming,” Journal of Statistical Planning and Inference, 141, 1684–1708.
   Web of Science ®Google Scholar
• Sturm, J. F. (1999), “Using SeDuMi 1.02, A Matlab Toolbox for Optimization Over Symmetric Cones,” Optimization Methods and Software, 11, 625–653.
   Web of Science ®Google Scholar
• Wang, R. H. (2000), “Approximate and Exact D-Optimal Designs for Multi-response Polynomial Regression Models,” Master Thesis, Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan.
   Google Scholar
• Wiens, D. P. (2015), “Robustness of Design,” in Handbook of Design and Analysis of Experiments, eds. A. Dean, M. Morris, J. Stufken, and D. Bingham, New York: CRC Press, pp. 719–753.
   Google Scholar
• Yang, M., Biedermann, S., and Tang, E. (2013), “On Optimal Designs for Nonlinear Models: A General and Efficient Algorithm,” Journal of the American Statistical Association, 108, 1411–1420.
   Web of Science ®Google Scholar
• Ye, J. J., Zhou, J., and Zhou, W. (2017), “Computing A-Optimal and E-Optimal Designs for Regression Models via Semidefinite Programming,” Communications in Statistics - Simulation and Computation, 46, 2011–2024.
   Web of Science ®Google Scholar
• Yin, Y. (2017), Theory and Algorithms for Finding Optimal Regression Designs. Ph.D. dissertation, Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada.
   Google Scholar
• Yue, R. X., and Liu, X. (2010), “IrL-Optimal Designs for a Hierarchically Ordered System of Regression Models,” Computational Statistics and Data Analysis, 54, 3458–3465.
   Web of Science ®Google Scholar
• Yue, R. X., Liu, X., and Chatterjee, K. (2014), “D-Optimal Designs for Multiresponse Linear Models With a Qualitative Factor,” Journal of Multivariate Analysis, 124, 57–69.
   Web of Science ®Google Scholar