In this survey, we describe the fundamental differential-geometric structures of information
manifolds, state the fundamental theorem of information geometry, and illustrate some use …

Functional data clustering is to identify heterogeneous morphological patterns in the
continuous functions underlying the discrete measurements/observations. Application of …

Function and shape data analysis are old topics in statistics, studied off and on over the last
several decades. However, the early years of the new millennium saw a renewed focus and …

A thoroughly revised and updated edition of this introduction to modern statistical methods
for shape analysis Shape analysis is an important tool in the many disciplines where objects …

The abundance of functional observations in scientific endeavors has led to a significant
development in tools for functional data analysis (FDA). This kind of data comes with several …

The Wasserstein metric, Wasserstein–Fréchet mean, simulation results and additional
proofs. The supplementary material includes additional discussion on the Wasserstein …

Constructing generative models for functional observations is an important task in statistical
functional analysis. In general, functional data contains both phase (or x or horizontal) and …

Recent developments in the probabilistic and statistical analysis of probability density
functions are reviewed. Density functions are treated as data objects for which suitable …

We consider the statistical analysis of trajectories on Riemannian manifolds that are
observed under arbitrary temporal evolutions. Past methods rely on cross-sectional analysis …

Amplitude and phase variation of point processes Page 1 The Annals of Statistics 2016, Vol.
44, No. 2, 771–812 DOI: 10.1214/15-AOS1387 © Institute of Mathematical Statistics, 2016 …