On the optimality of the simultaneous redundancy transformations

The objective of this paper is to introduce and motivate additional properties and interpretations for the redundancy variables. It is shown that these variables can be derived by application of certain invariance arguments and without reference to the index of redundancy. In addition, an optimality property for the variables is presented which is important whenever one restricts attention in a study to a subset of the redundancy variables. This optimality property pertains to the subset rather than to the individual variables.This paper is based in part on the author's doctoral dissertation, Department of Statistics, Princeton, University. Research was conducted under the supervision of Lawrence S. Mayer.