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Characterization of c‐, L‐ and ϕk‐optimal designs for a class of non‐linear multiple‐regression models
- Schmidt, Dennis
- Journal of the Royal Statistical Society 2019 v.81 no.1 pp. 101-120
- equations, nonlinear models, regression analysis
- Optimal designs for multiple‐regression models are determined. We consider a general class of non‐linear models including proportional hazards models with different censoring schemes, the Poisson and the negative binomial model. For these models we provide a complete characterization of c‐optimal designs for all vectors c in the case of a single covariate. For multiple regression with an arbitrary number of covariates, c‐optimal designs for certain vectors c are derived analytically. Using some general results on the structure of optimal designs for multiple regression, we determine L‐ and ϕk‐optimal designs for models with an arbitrary number of covariates.