Uniform Designs Limit Aliasing

When fitting a linear regression model to data, the effects not included in the model can confound those included in the model, resulting in incorrect estimates of the regression coefficients and incorrect inferences as to whether a term is significant. This paper shows how uniform designs can reduce this aliasing. The discrepancy is a quantitative measure of how uniformly design points are placed on an experimental domain. It is shown that in very general situations low-discrepancy designs limit aliasing. For the case of regular fractional factorial designs it is shown that minimum discrepancy designs have maximum resolution and minimum aberration. Since the concept of discrepancy is more general than resolution or aberration, discrepancy can be used to generalize the definitions of resolution and aberration to other types of designs.