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Characterization of c ‐, L ‐ and ϕ k ‐optimal designs for a class of non‐linear multiple‐regression models
Author(s) -
Schmidt Dennis
Publication year - 2019
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12292
Subject(s) - covariate , mathematics , censoring (clinical trials) , poisson regression , negative binomial distribution , generalized linear model , optimal design , poisson distribution , regression analysis , linear model , linear regression , class (philosophy) , statistics , characterization (materials science) , proper linear model , polynomial regression , computer science , population , artificial intelligence , materials science , nanotechnology , demography , sociology
Summary 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 ϕ k ‐optimal designs for models with an arbitrary number of covariates.