Peter Hall’s work on high-dimensional data and classification

Abstract

In this article, I summarise Peter Hall’s contributions to high-dimensional data, including their geometric representations and variable selection methods based on ranking. I also discuss his work on classification problems, concluding with some personal reflections on my own interactions with him. This article complements [Ann. Statist. 44 (2016) 1821–1836; Ann. Statist. 44 (2016) 1837–1853; Ann. Statist. 44 (2016) 1854–1866 and Ann. Statist. 44 (2016) 1867–1887], which focus on other aspects of Peter’s research.