A leap into functional Hilbert spaces with Harold Hotelling

The talk will focus on the problem of finite-sample null hypothesis significance testing on the mean element of a random variable that takes value in a generic separable Hilbert space. For this purpose, we will present a definition of Hotelling’s T2 statistic that naturally expands to any separable Hilbert space. In detail, we will present a unified framework for making inference on the mean element of Hilbert populations based on Hotelling’s T2 statistic, using a permutation-based testing procedure. We will then present the theoretical properties of the procedure (i.e., finitesample exactness and consistency) and show the explicit form of Hotelling’s T2 statistic in the case of some famous spaces used in functional data analysis like Sobolev and Bayes spaces.