Sticky central limit theorems on open books

By Thomas Hotz, Sean Skwerer, Stephan F. Huckemann, Huiling Le, James Stephen Marron, Jonathan C. Mattingly, Ezra Miller, James Nolen, M. Owen, Vic Patrangenaru. 2012

109 citations recorded by the source corpus.

Given a probability distribution on an open book (a metric space obtained by gluing a disjoint union of copies of a half-space along their boundary hyperplanes), we define a precise concept of when the Frechet mean (barycenter) is sticky. This nonclassical phenomenon is quantified by a law of large numbers (LLN) stating that the empirical mean eventually almost surely lies on the (codimension 1 and hence measure 0) spine that is the glued hyperplane, and a central limit theorem (CLT) stating that the limiting distribution is Gaussian and supported on the spine. We also state versions of the LLN and CLT for the cases where the mean is nonsticky (i.e., not lying on the spine) and partly sticky (i.e., is, on the spine but not sticky).

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2aece11e613757ef5261e6a0e0c6d39d65190293

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Benjamin Eltzner
2. Stephan F. Huckemann
3. Xavier Pennec
4. Emilie Chautru

In Statistics and Probability

1. James Stephen Marron
2. Stephan F. Huckemann
3. Benjamin Eltzner

Citations in the corpus

• A smeary central limit theorem for manifolds with application to high-dimensional spheres (2018, background): “3 Smeariness Recall from Huckemann (2015) that a sequence of random vectors Xn is k-th order smeary if n 1 Xn has a non-trivial limiting distribution as n→∞.”
• Persistent Homology Analysis of Brain Artery Trees (2014, background): “Hotz et al. (2013), followed by Barden, Le and Owen (2013, 2014), investigated surprising nonstandard central limit theory in phylogenetic tree spaces.”