An algebraic construction of minimally-supportedD-optimal designs for weighted polynomial regression

• Main Authors: Bo-jung Jiang, 姜柏仲
• Other Authors: F-C Chang
• Format: Others
• Language: en_US
• Online Access: http://ndltd.ncl.edu.tw/handle/17509565323744480048

碩士 === 國立中山大學 === 應用數學系研究所 === 92 === We propose an algebraic construction of $(d+1)$-point $D$-optimal designs for $d$th degree polynomial regression with weight function $omega(x)ge 0$ on the interval $[a,b]$. Suppose that $omega''(x)/omega(x)$ is a rational function and the information of whether the optimal support contains the boundary points $a$ and $b$ is available. Then the problem of constructing $(d+1)$-point $D$-optimal designs can be transformed into a differential equation problem leading us to a certain matrix including a finite number of auxiliary unknown constants, which can be solved from a system of polynomial equations in those constants. Moreover, the $(d+1)$-point $D$-optimal interior support points are the zeros of a certain polynomial which the coefficients can be computed from a linear system. In most cases the $(d+1)$-point $D$-optimal designs are also the approximate $D$-optimal designs.