Mainstream statistical methodology is generally applicable to data observed in Euclidean
space. There are, however, numerous contexts of considerable scientific interest in which …

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 …

Torus principal component analysis with applications to RNA structure Page 1 The Annals of
Applied Statistics 2018, Vol. 12, No. 2, 1332–1359 https://doi.org/10.1214/17-AOAS1115 © …

We study the problem of finding the global Riemannian center of mass of a set of data points
on a Riemannian manifold. Specifically, we investigate the convergence of constant step …

The (CLT) central limit theorems for generalized Fréchet means (data descriptors assuming
values in manifolds, such as intrinsic means, geodesics, etc.) on manifolds from the literature …

Diffusion means in geometric spaces Page 1 Bernoulli 29(4), 2023, 3141–3170 https://doi.org/10.3150/22-BEJ1578
Diffusion means in geometric spaces BENJAMIN ELTZNER1,a, PERNILLE EH HANSEN2,b …

Two central limit theorems for sample Fréchet means are derived, both significant for
nonparametric inference on non-Euclidean spaces. The first theorem encompasses and …

A Fréchet mean of a random variable Y with values in a metric space (Q, d) is an element of
the metric space that minimizes q↦ E d (Y, q) 2. This minimizer may be non-unique. We …

The task to write on data analysis on nonstandard spaces is quite substantial, with a huge
body of literature to cover, from parametric to nonparametrics, from shape spaces to …

We are interested in measures of central tendency for a population on a network, which is
modeled by a metric tree. The location parameters that we study are generalized Fr\'echet …