Optimal designs for rational models and weighted polynomial regression
有理模型与加权多项式回归的最优设计
In this paper $D$-optimal designs for the weighted polynomial regression model of degree $p$ with efficiency function $(1 + x^2)^{-n}$ are presented. Interest in these designs stems from the fact that they are equivalent to locally $D$-optimal designs for inverse quadratic polynomial models. For the unrestricted design space $\mathbb{R}$ and $p < n$, the $D$-optimal designs put equal masses on $p + 1$ points which coincide with the zeros of an ultraspherical polynomial,…