Exact D-optimal designs for weighted polynomial regression model

In this work, the exact D-optimal designs for weighted polynomial regression are investigated. In Gaffke (1987, J. Statist. Planning Inference 15, 189-204) a sufficient condition has been given that Salaeveskiǐ's type of result about the exact D-optimal designs holds when sample size n is large enough. Here we provide another sufficient condition for checking if Salaeveskiǐ's type of result still holds for weighted polynomial models, where it is a stronger condition and may not be as general as in Gaffke (1987, J. Statist. Planning Inference 15, 189-204) but can be used easily to give an efficient method to determine the sample size guaranteeing the result to be valid. A table of minimum sample sizes needed by our method is given for some weight functions, which are also shown numerically to be the same as the minimum sample sizes needed by Gaffke's condition in those cases. Finally for the no-intercept model as considered in Huang et al. (1995, Statistica Sinica, 441-458) the exact D-optimal designs on intervals [a,1],0≤a<1, and [-1,1] are also discussed.