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\noindent Statistica Sinica {\bf 16}(2006), 121-133

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\centerline{\large\bf OPTIMAL DESIGNS FOR  PARALLEL MODELS WITH }
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\centerline{\large\bf CORRELATED RESPONSES}
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\author{Mong-Na Lo Huang$^1$, Ray-Bing Chen$^2$, Chun-Sui Lin$^1$ and Weng Kee Wong$^3$}
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\centerline{\it $^1$National Sun Yat-sen University, $^2$National University of Kaohsiung}
\centerline{\it  and $^3$University of California at Los Angeles}
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\begin{quotation}
\noindent {\it Abstract:}
We consider  a parallel linear model with correlated dual
responses on a symmetric compact design region and construct
locally $D$-optimal designs for estimating the unknown parameters in
the model, and locally optimal designs for estimating the location
shift parameter. The $D$-optimal designs for the additive model are
invariant under linear transformation of the design space but
locally optimal designs for estimating the location shift do not
share this property. The latter
  optimal designs  depend on the correlation between the dual
responses  in an interesting and sensitive way.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
 approximate design,
biosassay, $D$-optimality, locally optimal design, location shift
parameter.\par
\end{quotation}

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