527
Views
0
CrossRef citations to date
0
Altmetric
Articles

Locally R-optimal designs for a class of nonlinear multiple regression models

ORCID Icon & ORCID Icon
Pages 107-120 | Received 09 Jun 2022, Accepted 27 Nov 2022, Published online: 12 Dec 2022

References

  • Atkinson, A. C., Donev, A. N., & Tobias, R. D. (2007). Optimum experimental designs, with SAS. Oxford University Press.
  • Chernoff, H. (1953). Locally optimal designs for estimating parameters. The Annals of Mathematical Statistics, 24(4), 586–602. https://doi.org/10.1214/aoms/1177728915
  • Dette, H. (1997). Designing experiments with respect to ‘standardized’ optimality criteria. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 59(1), 97–110. https://doi.org/10.1111/rssb.1997.59.issue-1
  • Fedorov, V. V. (1972). Theory of optimal experiments. Academic Press.
  • Freise, F., Gaffke, N., & Schwabe, R. (2021). The adaptive Wynn algorithm in generalized linear models with univariate response. The Annals of Statistics, 49(2), 702–722. https://doi.org/10.1214/20-AOS1974
  • Hao, H., Zhu, X., Zhang, X., & Zhang, C. (2021). R-optimal design of the second-order Scheffé mixture model. Statistics & Probability Letters, 173(C), 109069. https://doi.org/10.1016/j.spl.2021.109069
  • Idais, O., & Schwabe, R. (2021). Analytic solutions for locally optimal designs for gamma models having linear predictors without intercept. Metrika, 84(1), 1–26. https://doi.org/10.1007/s00184-019-00760-3
  • Kalish, L. A., & Harrington, D. P. (1988). Efficiency of balanced treatment allocation for survival analysis. Biometrics, 44(3), 815–821. https://doi.org/10.2307/2531593
  • Konstantinou, M., Biedermann, S., & Kimber, A. (2014). Optimal designs for two-parameter nonlinear models with application to survival models. Statistica Sinica, 24(1), 415–428. https://doi.org/10.5705/ss.2011.271
  • Li, K. H., Lau, T. S., & Zhang, C. (2005). A note on D-optimal designs for models with and without an intercept. Statistical Papers, 46(3),451–458. https://doi.org/10.1007/BF02762844
  • Liu, P., Gao, L. L., & Zhou, J. (2022). R-optimal designs for multi-response regression models with multi-factors. Communications in Statistics – Theory and Methods, 51(2), 340–355. https://doi.org/10.1080/03610926.2020.1748655
  • Liu, X., & Yue, R.-X. (2020). Elfving's theorem for R-optimality of experimental designs. Metrika, 83(4), 485–498. https://doi.org/10.1007/s00184-019-00728-3
  • Pukelsheim, F., & Torsney, B. (1993). Optimal weights for experimental designs on linearly independent support points. The Annals of Statistics, 19(3), 1614–1625. https://doi.org/10.2307/2241966
  • Radloff, M., & Schwabe, R. (2019). Locally D-optimal designs for non-linear models on the k-dimensional ball. Journal of Statistical Planning and Inference, 203, 106–116. https://doi.org/10.1016/j.jspi.2019.03.004
  • Russell, K. G., Woods, D. C., Lewis, S. M., & Eccleston, E. C. (2009). D-optimal designs for Poisson regression models. Statistica Sinica, 19(2), 721–730. https://doi.org/10.2307/24308852
  • Schmidt, D. (2019). Characterization of c-, L- and ϕk-optimal designs for a class of non-linear multiple-regression models. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 81(1), 101–120. https://doi.org/10.1111/rssb.12292
  • Schmidt, D., & Schwabe, R. (2015). On optimal designs for censored data. Metrika, 78(3), 237–257. https://doi.org/10.1007/s00184-014-0500-1
  • Schmidt, D., & Schwabe, R. (2017). Optimal design for multiple regression with information driven by the linear predictor. Statistica Sinica, 27(3), 1371–1384. https://doi.org/10.5705/ss.202015.0385
  • Silvey, S. D. (1980). Optimal design. Chapman and Hall.
  • Whittle, P. (1973). Some general points in the theory of optimal experimental designs. Journal of the Royal Statistical Society: Series B (Methodological), 35(1), 123–130. https://doi.org/10.1111/j.2517-6161.1973.tb00944.x
  • Yang, M., Biedermann, S., & Tang, E. (2013). On optimal designs for nonlinear models: A general and efficient algorithm. Journal of the American Statistical Association, 108(504), 1411–1420. https://doi.org/10.1080/01621459.2013.806268