Abstract
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 θ , or of a function of interest h ( θ ) , may be impossible with the singular design ξ * . Depending on how ξ * is approached by the empirical measure ξ n of the design points, with n the number of observations, consistency is achieved but the speed of convergence may depend on ξ n and on the value of θ . Even in situations where convergence is in 1 / n and the asymptotic distribution of the estimator of θ or h ( θ ) is normal, the asymptotic variance may still differ from that obtained from ξ * .
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