The paper "Comments on: shape-based functional data analysis" by Stöcker, Steyer, and Greven appeared at TEST
The paper Comments on: shape-based functional data analysis by Stöcker, A., Steyer, L. & Greven, S. appeared in TEST.
Introduction: We would first like to thank the authors, Yuexuan Wu, Chao Huang and Anuj Srivastava, for an interesting article, as well as for the relevant work, in particular on the square-root-velocity (SRV) framework, that it summarizes, and which we have found very useful in our own work. We consider the SRV framework a milestone in object data analysis.
While many aspects in the article are worthy of attention, we focus our discussion in the following on several aspects and challenges we have encountered in our work in this field. In particular, we will discuss the univariate versus the multivariate case in Sect. 2, the problem of sparsely sampled curves in Sect. 3, and regression respecting invariances in Sect. 4, before concluding with a discussion in Sect. 5.