ENBIS: European Network for Business and Industrial Statistics

Optimal designs for multifactor and heteroscedastic regression models

22 September 2009, 11:40 – 12:10

Abstract

Submitted by

ISABEL ORTIZ

Authors

Carmelo Rodriguez Torreblanca; Isabel Maria Ortiz Rodriguez; Ignacio Martinez Lopez

Affiliation

University of Almeria-Spain

Abstract

The research on optimal experimental designs for nonlinear
regression models is of great interest because these models are used
to characterize chemical, biological or agricultural phenomena. Much
of them involve an exponential decay. In Optimal Experimental Design
theory the use of non-linear models is far more complex than the case
of linear ones, due to the fact that in the first case the best design
will depend on the values of the unknown parameters. In the homoscedastic
case the errors are assumed independent and identically distributed,
with zero mean and constant variance. The heteroscedastic model allows
a more complex structure for the variance, and the treatment is more
difficult.

Moreover, most experiments are described by multi-factor models and the
construction of optimum designs is more complicated for these
models than for models with a single factor. Therefore, it is
interesting to obtain optimum designs for multi-factor models in
terms of optimum designs for their one-dimensional components.

In this paper we will center on heteroscedastic exponential
multi-factor regression models.

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