Optimal designs for quadratic regression (Q1821464)

For quadratic regression on the symmetric unit interval optimal designs are computed for all subsets of components of the parameter vector. The optimality criteria considered are the p-means of the information matrices for the parameters of interest, with -\(\infty \leq p\leq 1\). It turns out that it suffices to consider a one-dimensional class of designs depending on a single weight \(\alpha\) only. We compute and graph the optimal weight \(\alpha\) (p) and the optimal information value \(\nu\) (p) for each subset of components of the parameter vector. The graphs of these functions show some surprising peculiarities and are discussed. Other criteria based on generalized means are mentioned briefly.