An algebraic construction of minimally-supportedD-optimal designs for weighted polynomial regression
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...
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| Format: | Others |
| Language: | en_US |
| Online Access: | http://ndltd.ncl.edu.tw/handle/17509565323744480048 |
| Summary: | 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.
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