Optimal Characteristic Designs for Polynomial Models

Abstract

Using the characteristic polynomial coefficients of the inverse of the information matrix, design criteria can be defined between A- and D-optimality (Lopez-Fidalgo and Rodriguez-Diaz, 1998). With a slight modification of the classical algorithms, the gradient expression allows us to find some optimal characteristic designs for polynomial regression. We observe that these designs are a smooth transition from A- to D-optimal designs. Moreover, for some of these optimal designs, the efficiencies for both criteria, A- and D-optimality, are quite good. Nice relationships emerge when plotting the support points of these optimal designs against the number of parameters of the model. In particular, following the ideas developed by Pukelsheim and Torsney (1991), we have considered A-optimality. Another mathematical expression can be given for finding A-optimal support points using nonlinear regression. This could be very useful for obtaining optimal designs for the other characteristic criteria.