Optimum design theory sometimes yields singular designs. An example with a linear regression model often mentioned in the literature is used to illustrate the difficulties induced by such designs. The estimation of the model parameters [theta], or of a function of interest h([theta]), may be...

In this paper we consider optimal design of experiments in the case of correlated observations, when no replications are possible. This situation is typical when observing a random process or random field with known covariance structure. We present a theorem which demonstrates that the...