| Summary: | 碩士 === 國立中山大學 === 應用數學研究所 === 86 === This thesis is divided into the following two parts.In the first part of this work, optimal extrapolation design problems inpolynomial regression models are considered. If there is uncertaintyin the degree of the polynomial, a class of robust optimal designcriteria for extrapolation motivated in part by Kiefer's $L_p$-classof optimality criteria proposed in Dette and Wong (1996) is considered.Here, we study the performances of convex combination of individualoptimal design to see if the optimal convex combination would yield anoptimal or at least efficient designs.In the second part of this work, $D$- and $D_s$- optimal designproblems in linear regression models with a one-dimensional controlvariable and an $k$-dimensional response variable $Y=(Y_1, \cdots, Y_k)$are considered. The components of $Y$ are correlated with knowncovariance matrix. We will first discuss $D$- and $D_s$- optimal designsfor estimating the unknown common parameters in the cases with polynomialmodels in two response variables. The $D$- and $D_s$- optimal designsare found explicitly in some low degree cases where the number of supportsfor the optimal design depend critically on the covariance structure.We also investigate locally $D$-optimal design for some nonlinearmultiresponse models as discussed in Draper and Hunter (1966).\
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