Design admissibility and de la Garza phenomenon in multi-factor experiments
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Date
2020
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Abstract
The determination of an optimal design for a given regression problem is an intricate
optimization problem, especially for models with multivariate predictors. Design
admissibility and invariance are main tools to reduce the complexity of the optimization
problem and have been successfully applied for models with univariate predictors.
In particular several authors have developed sufficient conditions for the existence of
saturated designs in univariate models, where the number of support points of the optimal
design equals the number of parameters. These results generalize the celebrated de
la Garza phenomenon (de la Garza, 1954) which states that for a polynomial regression
model of degree p -1 any optimal design can be based on at most p points.
This paper provides - for the first time - extensions of these results for models
with a multivariate predictor. In particular we study a geometric characterization
of the support points of an optimal design to provide sufficient conditions for the
occurrence of the de la Garza phenomenon in models with multivariate predictors and
characterize properties of admissible designs in terms of admissibility of designs in
conditional univariate regression models.
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Keywords
admissibility, optimal design, multi-factor experiment, conditional model, dual problem