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Central limit theorems for Fréchet means in the space of phylogenetic trees


 
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1. Title Title of document Central limit theorems for Fréchet means in the space of phylogenetic trees
 
2. Creator Author's name, affiliation, country Dennis Barden; University of Cambridge; United Kingdom
 
2. Creator Author's name, affiliation, country Huiling Le; University of Nottingham; United Kingdom
 
2. Creator Author's name, affiliation, country Megan Owen; University of Waterloo; Canada
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) central limit theorem; Frechet mean; phylogenetic trees; stratified manifold.
 
3. Subject Subject classification 60D05; 60F05
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
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7. Date (YYYY-MM-DD) 2013-02-16
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2201
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2201
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
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