Exact D-optimal designs for polynomial regression without intercept

Abstract

For the regression model fk(x)=(x,x2,…,xk)T on [a,1],−1⩽a<1, the exact n-point D-optimal designs are proved to be ones that put mass as equally as possible among the support points of the approximate D-optimal design for fk(x) if n⩾k,a=−1 and k=2,4, if n⩾k,a⩾(2−10)/6 and k=2, and if n⩾2k,−0.0876991⩽a⩽(5−1)/25 and k=3. For the other cases, the properties of exact D-optimal designs are discussed on the basis of an intensive numerical study.