Information Increasing Orderings in Experimental Design Theory
Friedrich Pukelsheim · International Statistical Review · 1987
A survey is given on recent results to identify order relations for experimental designs which appiopriately describe when one design is more informative than another one.The tschnique is to augment the usual Loewner ordering of information matrices through group majorization where the group is such that it reflects the symmetries inherent in the underlying problem.Information increasing orderings appear to be a helpful tool to systematically improve on a given design, they may also be used to motivate special criteria such as the classical determinant criterion, and they sometimes aid in idenitifying optimal designs or at least complete classes.