Comments on: Recent advances in directional statistics

Abstract Inspired by this felicitous, highly concentrated and rather exhaustive review of a rapidly growing field, many larger research areas that warrant further investigation come to mind. In comment, three are selected: fully satisfactory PCA on tori polyspheres, harnessing linearity through Lie algebras underlying homogeneous spaces such as those for directional data, statistical analysis based critical points (e.g. mode antimodes) Fréchet $$L^p$$ L p -functions.