An Application of Majorization to the Problem of Selecting the Largest Interaction in a Two-Factor Experiment.
CORNELL UNIV ITHACA N Y DEPT OF OPERATIONS RESEARCH
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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.
- Statistics and Probability