An Application of Majorization to the Problem of Selecting the Largest Interaction in a Two-Factor Experiment.

摘要

The problem of devising a single-stage procedure for the goal of selecting the factor-level combination associated with the largest positive interaction is studied for the usual linear model underlying a 2-factor rxc (r > or = 2, c > or = 3) experiment involving qualitative variables when the common variance is known. The main result of the present paper is a theorem which gives this least favorable (LF)-configuration explicitly for the 2xc case; the principal tool used in the proof of the theorem is the theory of Schur-concavity and majorization in multivariate distributions as described by Marshall and Olkin. Various generalizations are proposed.