Generalized projection discrepancy and its applications in experimental designs

The objective of this paper is to study the issue of the generalized projection discrepancy along the line of Qin et al. (J Stat Plan Inference 142:1170-1177, 2012) based on generalized discrete discrepancy measure proposed by Chatterjee and Qin (J Stat Plan Inference 141:951-960, 2011). We shall study the projection properties for general asymmetric factorials and provide some analytic connections between minimum generalized projection uniformity and other optimality criteria. A new lower bound on the generalized projection discrepancy for asymmetric factorials is presented here.