Augmented designs to choose between constant absolute and relative errors and to estimate model parameters

In experimental sciences such as chemistry, the measurement error may be homoscedastic or heteroscedastic. The data should be collected with the goal of identifying the right error-variance structure, as an incorrectly specified model would lead to wrong conclusions. A design criterion that reflects this goal is KL-optimality. Frequently, however, KL-optimum designs are wholly inefficient for other inferential purposes, such as precise estimation. In this case, the addition of some experimental points might be convenient. This work focuses on the enrichment of a design through the inclusion of some additional support points, with the goal of guaranteeing a minimum KL-efficiency to be able to optimally choose between different variance specifications. This strategy is also useful for modifying a design that is already available, for instance a D-optimal design, to manage the problem of correct error-variance specification.