E-OPTIMAL DESIGNS IN WEIGHTED POLYNOMIAL REGRESSION

Based on a duality between E-optimality for (sub-) parameters in weighted polynomial regression and a nonlinear approximation problem of Chebyshev type, in many cases the optimal approximate designs on nonnegative and nonpositive experimental regions [a, b] are found to be supported by the extrema of the only equioscillating weighted polynomial over this region with leading coefficient 1. A similar result is stated for regression on symmetric regions [-b, b] for certain subparameters, provided the region is ''small enough,'' for example, b less than or equal to 1. In particular, by specializing the weight function, we obtain results of Pukelsheim and Studden and of Dette.