RECURRENCE MOMENT FORMULAS FOR D-OPTIMAL DESIGNS

We derive recurrence formulas for the moments of the D-optimal designs for the polynomial model of degree k under different assumptions on t he heteroscedastic structure. A new proof for deriving the asymptotic optimal designs as k tends to infinity is given. We also show these re currence formulas are useful for identifying the asymptotic optimal de signs in other settings, including limiting model robust optimal desig ns.