Robustness and accuracy of methods for high dimensional data analysis based on Student's t-statistic

Abstract

Student's t-statistic is finding applications today that were never envisaged when it was introduced more than a century ago. Many of these applications rely on properties, e.g. robustness against heavy-tailed sampling distributions, that were not explicitly considered until relatively recently. We explore these features of the t-statistic in the context of its application to very high dimensional problems, including feature selection and ranking, the simultaneous testing of many different hypotheses and sparse, high dimensional signal detection. Robustness properties of the t-ratio are highlighted, and it is established that those properties are preserved under applications of the bootstrap..