Limit theorems for the inductive mean on metric trees (CROSBI ID 152846)
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Podaci o odgovornosti
Basrak, Bojan
engleski
Limit theorems for the inductive mean on metric trees
In 2003 Sturm proved that the barycenter of the probability distribution on metric spaces with non-positive curvature can be consistently estimated by inductive sample means. In this article we consider the limiting behavior of these means in the case of metric trees. Our main result presents the asymptotic distribution for the inductive means and shows that it exhibits a phase transition phenomenon for certain changes of the underlying distribution. Moreover, for this particular case, the paper relaxes necessary conditions for the strong law of large numbers obtained by Sturm.
limit theorems ; binary trees ; global NPC spaces ; inductive means ; convergence in distribution
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Podaci o izdanju
47 (4)
2010.
1136-1149
objavljeno
0021-9002
1475-6072
10.1239/jap/1294170525