Asymptotic data analysis on manifolds

Harrie Hendriks, Zinoviy Landsman

Research output: Contribution to journalArticlepeer-review


Given an m-dimensional compact submanifold M of Euclidean space R s, the concept of mean location of a distribution, related to mean or expected vector, is generalized to more general Rs-valued functionals including median location, which is derived from the spatialmedian. 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.

Original languageEnglish
Pages (from-to)109-131
Number of pages23
JournalAnnals of Statistics
Issue number1
StatePublished - Feb 2007


  • Compact submanifold of Euclidean space
  • Confidence region
  • Cutlocus
  • Mean location
  • Median location
  • Multivariate Lindeberg condition
  • Spatial median
  • Sphere
  • Spherical distribution
  • Stabilization
  • Stiefel manifold
  • Weingarten mapping

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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