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Student's $t$ statistic is finding applications today that were neverenvisaged when it was introduced more than a century ago. Many of theseapplications rely on properties, for example robustness against heavy tailedsampling distributions, that were not explicitly considered until relativelyrecently. In this paper we explore these features of the $t$ statistic in thecontext of its application to very high dimensional problems, including featureselection and ranking, highly multiple hypothesis testing, and sparse, highdimensional signal detection. Robustness properties of the $t$-ratio arehighlighted, and it is established that those properties are preserved underapplications of the bootstrap. In particular, bootstrap methods correct forskewness, and therefore lead to second-order accuracy, even in the extremetails. Indeed, it is shown that the bootstrap, and also the more popular butless accurate $t$-distribution and normal approximations, are more effective inthe tails than towards the middle of the distribution. These propertiesmotivate new methods, for example bootstrap-based techniques for signaldetection, that confine attention to the significant tail of a statistic.

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