Translator Disclaimer
December 2015 A diffusion process associated with Fréchet means
Huiling Le
Ann. Appl. Probab. 25(6): 3033-3046 (December 2015). DOI: 10.1214/14-AAP1066

Abstract

This paper studies rescaled images, under $\exp^{-1}_{\mu}$, of the sample Fréchet means of i.i.d. random variables $\{X_{k}\vert k\geq 1\}$ with Fréchet mean $\mu$ on a Riemannian manifold. We show that, with appropriate scaling, these images converge weakly to a diffusion process. Similar to the Euclidean case, this limiting diffusion is a Brownian motion up to a linear transformation. However, in addition to the covariance structure of $\exp^{-1}_{\mu}(X_{1})$, this linear transformation also depends on the global Riemannian structure of the manifold.

Citation

Download Citation

Huiling Le. "A diffusion process associated with Fréchet means." Ann. Appl. Probab. 25 (6) 3033 - 3046, December 2015. https://doi.org/10.1214/14-AAP1066

Information

Received: 1 July 2013; Revised: 1 September 2014; Published: December 2015
First available in Project Euclid: 1 October 2015

zbMATH: 1328.58035
MathSciNet: MR3404630
Digital Object Identifier: 10.1214/14-AAP1066

Subjects:
Primary: 60D05, 60F05

Rights: Copyright © 2015 Institute of Mathematical Statistics

JOURNAL ARTICLE
14 PAGES


SHARE
Vol.25 • No. 6 • December 2015
Back to Top