Academic

Abstract

Qualitative descriptions of the shape of a function (e.g., convex, monotone, bimodal) and their use in assessing methodological tools abound in functional data analysis. The shape of functional data is tied to its amplitude, and one way to quantify it is through a registration or alignment procedure; another is to work directly with the shape space that treats phase variation as nuisance. I will discuss a stratified geometry for the shape space of (smooth) functions, under which the space can have regions of non-positive and (positive) unbounded curvature,  and examine its implications on aspects of statistical modelling of functional data in the presence of phase variation.