Efficiency comparisons in linear inference

Abstract

A new approach to comparative design efficiency is given in linear estimation and in tests for linear hypotheses. In contrast to others, this approach gives a complete assessment of two designs for any model on identifying precisely the subspaces of parameters for which one design is more efficient than another, or two designs are equally efficient. Local and global bounds on relative design efficiencies are given with reference to these subspaces, and connections to information functionals are noted. The relative influences of design points with regard to deletion and augmentation are examined and related to measures of influence from the literature. Our approach provides numerical diagnostics for use in design evaluation before an experiment has been run. The concepts are illustrated with reference to selected second-order designs.