Rauf Ahmad: High-dimensional multivariate analysis and the theory of U-statistics

Analysis of high-dimensional multivariate data is relatively new but still much sought after area of research with applications extending as wide as into the realms of genetics, medicine, even engineering and agriculture. This, however, also pertains to the fact the methodological development in this area, particularly the asymptotics, is relatively not so well-charted territory and different researchers focus from different aspects. This talk concentrates on such an analysis by the use of $U$-statistics theory. Further, the gist of the talk will fundamentally focus on two crucial points: One (general), how the theory, particularly the properties of the newly proposed test statistic, is affected by the assumptions we make, and two (specific), how the U-statistic theory helps solve these problems and give more insight into the new problems that arise. As a particular example, it will be shown how the mean-testing problem under high-dimensionality is fixed by the use of U-statistics theory by taking care of complete Behrens-Fisher problem into account and without assuming normality. In this sense, the talk will target these specific points more than giving technical details of test statistics which are available in detail in the papers/reports.