A note on all-bias designs with applications in spline regression models

If a model is fitted to empirical data, bias can arise from terms which are not incorporated in the model assumptions. As a consequence the commonly used optimality criteria based on the generalized variance of the estimate of the model parameters may not lead to efficient designs for the statistical analysis. In this note some general aspects of all-bias designs are presented, which were introduced in this context by Box and Draper (1959). We establish sufficient conditions such that a given design is an all-bias design and illustrate these in the special case of spline regression models. In particular our results generalize recent findings of Woods and Lewis (2006).