Asymptotic data analysis on manifolds

Details Asymptotic data analysis on manifolds Asymptotic data analysis on manifolds

2007-08-03

arxiv.org/abs/0708.0474v1

Annals of Statistics 2007, Vol. 35, No. 1, 109-131

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000000993 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053606000000993

Given an m-dimensional compact submanifold $\mathbf{M}$ of Euclidean space $\mathbf{R}^s$, the concept of mean location of a distribution, related to mean or expected vector, is generalized to more general $\mathbf{R}^s$-valued functionals including median location, which is derived from the spatial median. The asymptotic statistical inference for general functionals of distributions on such submanifolds is elaborated. Convergence properties are studied in relation to the behavior of the underlying distributions with respect to the cutlocus. An application is given in the context of independent, but not identically distributed, samples, in particular, to a multisample setup.

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