Tools for Characterizing the Supports and their Sizes for Nonlinear D-Optimal Designs

For a k-parameter nonlinear model, the minimum number of support points for any D-optimal design is between k and k(k+1)/2. Identification and classification of cases with minimum support points are of great interest to both theoreticians and practitioners. Although the literature contains examples of minimum points D-optimal designs. In this paper, we utilize analytical tools, Tchebycheff system, and maximum principle to provide some sufficient conditions such that the D-optimal design is precisely supported by 2 points. The models we consider include generalized linear models, nonlinear regression models with normal error, and a special subclass of general nonlinear model.