Exact d-optimal design under response variable transformation

In experimental sciences, optimal designs, which focus on the efficiency of specific properties, are alternatives of fundamental importance when the practical problem involves some complexity not directly contemplated in the classical design formulation. Most of the methods assumes homogeneity of variances, which is not always verified in the data set. The aim of this work is to develop a methodology to construct exact optimal or efficient designs in situations of nonhomogeneous variances. It is assumed that application of a transformation from the Box-Cox family accomplishes both linearity and homocedasticity. Results for several examples assuming first and second order models are presented and discussed.