Admissibility and consistency for multiple comparison problems with dependent variables

In response to the need of dealing with high dimensional data, new multiple testing procedures (MTPs) based on p-values were developed to improve average power while controlling error rates at the same time. Although MTPs are well accepted and practiced in many disciplines, little attention has been put on a decision theory approach to evaluate MTPs. In a series of papers, Cohen and Sackrowitz (2005a,2005b,2007,2008} laid out the foundation to assess MTPs by studying both type I and type II errors. Here we extend that work and focus on some properties, such as admissibility, p-value monotonicity and consistency, to assess frequently used and new MTPs. Applications include all-pairwise comparisons in anova models and change point problems. In addition, the development of admissible procedures for a matrix order problem is presented.Ph.D.Includes bibliographical referencesIncludes vitaby Kuo-mei Che