Computation of c-optimal designs under correlation

J. M. Rodríguez Díaz

In the optimal design of experiments setup different optimality criteria can be considered. One of the most used is c-optimality,
that for a given model looks for the design that minimizes the variance of the linear combination
of the parameters' estimators given by vector c. c-optimal designs are needed when dealing
with standardized criteria, and are specially useful when taking c as the Euclidean vectors
since in that case they provide the best designs for estimating each one of the parameters.
The nice procedure proposed by Elfving for independent observations is the origin of the idea
of the procedure that can be used in the correlation framework.
Some analytical results are shown for the case of constant covariance,
but even for this case the computational task becomes quite hard when moving from the simpler models.
For this reason an algorithmic procedure is proposed that can be used when dealing with more complex models
and for some covariance structures.

Palabras clave: c-optimality criteria correlated observations Elfving's method linear model variance- covariance matrix

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