ABSTRACT OF THE DISSERTATION Multiple testing methods in dependent cases

The most popular multiple testing procedures are stepwise procedures based on P-values for individual test statistics. Included among these are the false discovery rate (FDR) controlling procedures of Benjamini-Hochberg(1995) and their offsprings. For many models including the case where model variables are multivariate normal, dependent and alternatives are two sided, these stepwise procedures lack an intuitive convexity property which is also needed for admissibility. Here we present two new stepwise methods that do in fact have the convexity property. Furthermore unlike the method using P-values based on marginal distributions, the new methods take dependency into account in all stages. Still further the new methodology is computationally feasible. Applications are detailed for models such as testing for change points of variances and testing treatments against control of variances. ii Acknowledgements I would like to express my deepest thanks to Professor Arthur Cohen and Professor Harold B. Sackrowitz for bringing me to this interesting field of multiple hypotheses testing, for encouraging, patiently guiding me and discussing problems with me almost every day. Through doing the research with them for these two years, I learned not only the knowledge and analytical skills but also the strong will and indomitable spirit to solve difficult problems. The two years research work is really a happy and unforgettable experience to me. Also I’d like to thank my husband, Jixin Li for continuous encouragement and support. ii