@article{EJP2201,
author = {Dennis Barden and Huiling Le and Megan Owen},
title = {Central limit theorems for Fréchet means in the space of phylogenetic trees},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {18},
year = {2013},
keywords = {central limit theorem; Frechet mean; phylogenetic trees; stratified manifold.},
abstract = {This paper studies the characterisation, and the limiting distributions, of Fréchet means in the space of phylogenetic trees. This space is topologically stratified, as well as being a CAT(0) space. We use a generalised version of the Delta method to demonstrate non-classical behaviour arising from the global topological structure of the space. In particular, we show that, for the space of trees with four leaves, although they are related to the Gaussian distribution, the forms taken by the limiting distributions depend on the co-dimensions of the strata in which the Fréchet means lie.},
pages = {no. 25, 1-25},
issn = {1083-6489},
doi = {10.1214/EJP.v18-2201},
url = {http://ejp.ejpecp.org/article/view/2201}}