Date of Award

Fall 2017

Document Type


Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)


Mathematical Sciences

First Advisor

Sunil Kumar Dhar

Second Advisor

Wenge Guo

Third Advisor

Ji Meng Loh

Fourth Advisor

Sundarraman Subramanian

Fifth Advisor

Satrajit Roychowdhury


In applications such as studying drug adverse events (AE) in clinical trials and identifying differentially expressed genes in microarray experiments, the data of the experiments usually consists of frequency counts. In the analysis of such data, researchers often face multiple hypotheses testing based on discrete test statistics. Incorporating this discrete property of the data, several stepwise procedures, which allow to use the CDF of p-values to determine the testing threshold, are proposed for controlling familiwise error rate (FWER). It is shown that the proposed procedures strongly control the FWER and are more powerful than the existing ones for discrete data. Through some simulation studies and real data examples, the proposed procedures are shown to outperform the existing procedures in terms of the FWER control and power. An R package “MHTdiscrete” and a web application are developed for implementing the proposed procedures for discrete data.

Included in

Mathematics Commons