Statistical analyses for ranking data

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a) Pathway analysis of microarray data. The statistical analysis of microarray data can potentially provide vital information for flagging genes that play important biological roles in the development of a complex disease. In this research, we plan to incorporate the biology at the initial stage by focusing on pathways or functional enrichment of microarray data as a way to take into account meaningful groupings of genes. An analysis of pathways can help to identify subtle changes in the expression of a group of genes for which the biological interpretation is more apparent. The approach being proposed is entirely nonparametric in nature and takes into account correlations which naturally exist among genes. b) The comparison of two groups having an umbrella ordering. In a recent article, a general method was developed and evaluated for constructing nonparametric tests of hypotheses for "umbrella alternatives". Such alternatives arise in situations where the treatment effect changes in direction after reaching a peak. In the present research, we compare two populations which exhibit an umbrella ordering and develop in part a test of the hypothesis that they have the same peak, whether or not its location is known. c) Nonparametric classification problems based on the ranks of the data. In this research, we treat the well-known classification problem involving two or more populations but propose to use only the ranks of the data.