Statistical methods for gene selection using differential gene expression and building gene co-expression networks:

This thesis investigates three most challenging statistical problems that relate to three important stages of the pipeline of DNA microarray data analysis which are identification of differentially expressed genes, determination of sample size based on specified power, desired fold change and given error rate, and construction of gene co-expression network. At the center of these methods is a new version of the Stochastic Approximation methodology that works for distribution functions. The method is applied to estimation problems in the conditional-t procedure (Amaratunga and Cabrera (2003)) and in the estimation of the covariance matrix. The new covariance estimates are applied to the estimation of gene co-expression network (Zhang and Hovarth(2005)). In both cases the new method results in substantial improvement in performance. This is shown in several simulations that are presented throughout the thesis. In addition we show examples from real applications to illustrate the main results.Ph.D.Includes bibliographical references (p. 83-87)by Zhaoyu Lu