| Summary: | 碩士 === 國立中山大學 === 應用數學研究所 === 84 === For cubic regression without an intercept on the symmetric
interval $[-a,a]$, $phi_p$-optimal designs $(-inftyleq p
leq 1)$ are computed for six parameter subsystems. For the
present setting, it sufficies to consider a two-dimensional
class of symmetric designs depending on two parameters. The
$D$-, $E$- and $T$-optimal designs for all parameter subsystems
are found and numerically optimal designs for some selected
values of $a$ are computed. Some special properties of these
optimal discussed. In particular, the $D$-optimal designs are
invariant under scaling the interval. Moreover, the asymptotic
properties of the optimal designs are also derived as $a o
infty$ and $a o 0$. Finally, the efficiency of a $phi_p$-
optimal design, when it compares with a $phi_q$-optimal
design, is also investigated.
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