Discussion contribution "Functional models for time-varying random objects'' by Dubey and Müller (to appear in JRSS-B)

In an inspiring paper Dubey and M\"uller (DM) extend PCA to the case that observations are metric-valued functions. As an alternative, we develop a kernel PCA approach, which we show is closely related to the DM approach. While kernel principal components (kPCs) are simply defined, DM require added complexity in the form of "object FPCs'' and "Fr\échet scores".