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\footnotesize \noindent Statistica Sinica {\bf 19} (2009), 1587-1601

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\normalsize
 \centerline{\large\bf OPTIMAL DESIGNS FOR ESTIMATING PAIRS OF}
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 \centerline{\large\bf COEFFICIENTS IN FOURIER REGRESSION MODELS}
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 \author{Holger Dette$^1$, Viatcheslav B. Melas$^2$ and Petr Shpilev$^2$}
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 \centerline{\it $^1$Ruhr-Universit\"at Bochum and $^2$St. Petersburg State University}
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\begin{quotation}
\noindent {\it Abstract:} In the common Fourier regression model we
investigate the optimal design problem for estimating pairs of the
coefficients, where the explanatory variable varies in the interval
$[-\pi, \pi]$. $L$-optimal designs are considered and for many
important cases $L$-optimal designs can be found explicitly, where
the complexity of the solution depends on the degree of the
trigonometric regression model and the order of the terms for which
the pair of the coefficients has to be estimated. \par
 \vspace{9pt}
 \noindent
{\it Key words and phrases:} Equivalence theorem, Fourier regression
models, $L$-optimal designs, parameter subsets.
\par
\end{quotation}

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