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\noindent Statistica Sinica {\bf 11}(2001), 261-272
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\centerline{\large\bf TWO ROBUST DESIGN APPROACHES}
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\centerline{\large\bf FOR LINEAR MODELS WITH CORRELATED ERRORS}
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\centerline{Julie Zhou}
\vspace{.4cm}
\centerline{\it University of Victoria}
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\begin{quotation}
\noindent {\it Abstract:}
In this paper,
infinitesimal and minimax approaches are used to
construct robust regression designs for linear models with correlated
errors.  We consider IMSE (Integrated Mean Squared Error) as the
loss function.  Using an infinitesimal approach, we minimize  IMSE
at the ideal model subject to two robust constraints to derive
M-robust designs.   We also minimize the maximum
of the IMSE to obtain minimax designs.  In particular,
M-robust and minimax designs are constructed for an approximately
linear model with MA(1) errors.  These designs are robust against
small departures from the assumed regression response and small departures
from the assumption of uncorrelated errors.
It is interesting that  M-robust  and  minimax
designs have the same form of density function,
while M-robust designs require less restrictive ordering of design points.
Implementation is discussed and examples are given.\par
\vspace{9pt} \noindent {\it Key words and phrases:}
Approximately linear regression response, infinitesimal approach,
M-robust design, minimax design, moving average errors,
robust regression design. \par
\end{quotation}
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