Statistical methods for the analysis of high-dimensional data

© 2010 Dr. Hugh Richard MillerHigh-dimensional statistics has captured the imagination of many statisticians worldwide, because of its interesting applications as well as the unique challenges faced. This thesis addresses a range of problems in the area, integrated into an overall framework. Problems explored include how to effect feature selection and test variable relationships, particularly when important nonlinearities may be present; how to create a nonparametric model that adapts to the observed importance of different variables in a dataset; how to assess the reliability of a ranking, for example how to list genes in order of importance to a disease, and how to determine circumstances where we can expect parts of this ranking to be reliable; how to perform hypothesis tests on extremes of populations; and how to incrementally build a multivariate model in high-dimensional situations while simultaneously protecting against overfitting. These problems are addressed through both theoretical and numerical means