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2015-19

Optimal Design for Multiple Regression with Information Driven by the Linear Predictor

by Schmidt, D.; Schwabe, R..


Series: 2015-19, Preprints

MSC:
62K05 Optimal designs
62N01 Censored data models

Abstract:
In this paper we consider nonlinear models with an arbitrary number of
covariates for which the information additionally depends on the value of the
linear predictor. We establish the general result that for many optimality
criteria the support points of an optimal design lie on the edges of the design
region, if this design region is a polyhedron. Based on this result we show
that under certain conditions the D-optimal designs can be constructed from
the D-optimal designs in the marginal models with single covariates. This
can be applied to a broad class of models, which include the Poisson, the
negative binomial as well as the proportional hazards model with both type
I and random censoring.

Keywords:
multiple regression model, D -optimality, censored data, pro- portional hazards model, generalized linear models