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

Evolution sometimes results in discrete morphological differences among populations that
diverge from a common source. This “saltation” can occur with features quantified by …

The asymptotic concentration of the Fr {\'e} chet mean of IID random variables on a Rieman-
nian manifold was established with a central limit theorem by Bhattacharya\& Patrangenaru …

Although manifold statistics is an established tool for computational anatomy, a number of
structures are not well modeled on manifolds. Examples include data with variable …

Classical statistical theory has been developed under the assumption that the data belongs
to a linear space. However, in many applications the intrinsic geometry of the data is more …

We investigate a geometric computational framework, called the “scaling-rotation
framework”, on Sym^+(p), the set of p*p symmetric positive-definite (SPD) matrices. The …

Given a random object on a stratified space, one defines the Fréchet mean, the Fréchet
antimeanand additional population parameters associated withits Fréchet function, in case …

For 1≤ p≤∞, the Fréchet p-mean of a probability measure on a metric space is an
important notion of central tendency that generalizes the usual notions in the real line of …

Fr\'echet means of samples from a probability measure $\mu $ on any smoothly stratified
metric space M with curvature bounded above are shown to satisfy a central limit theorem …

Statistical inference for manifolds attracts much attention because of its power of working
with more general forms of data or geometric objects. We study regression and stochastic …