Many results on optimal designs are derived under the assumption that the statistical model is known at the design stage. However, rarely is the researcher confident that a particular model underlies the data. Thus, the purpose of the experiment is to determinate which of the models is more adequate. T-optimality criterion given by Atkinson and Fedorov (1975a,b) is a method used to discriminate between two or several linear regression with normal errors, one of which is taken "true". In order to discriminate between two non- normal models, a criterion based on KL- distance is proposed, the KL- criterion.
When the problem is to discriminate between two separate models with no nesting, the compound KL- criterion is used. In this way is avoided the dependence on the choice of the "true" model. A generalization of the KL- criterion to discriminate among several non-normal models is proposed in Tommasi (2007).
The designs obtained with the KL-optimality criterion are optimal for model discrimination but may be inadequate for parameter estimation. DT optimal design criterion (Atkinson, 2007) provides an alternative for the dual problem of model discrimination and parameter estimation. This criterion considers the geometric mean of the T and D-efficiencies. In this work an alternative criteria is given using the weighted arithmetic mean of KL- and D- efficiencies.
Finally one generalization of the DT-criterion is provided in order to deal with the problem of the discrimination between several models and parameters estimation. Real data applications coming from biological and medical experiments are used to illustrate the different criteria.