Mean Location and Sample Mean Location on Manifolds: Asymptotics, Tests, Confidence Regions

Harrie Hendriks, Zinoviy Landsman

Research output: Contribution to journalArticlepeer-review

Abstract

In a previous investigation we studied some asymptotic properties of the sample mean location on submanifolds of Euclidean space. The sample mean location generalizes least squares statistics to smooth compact submanifolds of Euclidean space. In this paper these properties are put into use. Tests for hypotheses about mean location are constructed and confidence regions for mean location are indicated. We study the asymptotic distribution of the test statistic. The problem of comparing mean locations for two samples is analyzed. Special attention is paid to observations on Stiefel manifolds including the orthogonal groupO(p) and spheresSk-1, and special orthogonal groupsSO(p). The results also are illustrated with our experience with simulations.

Original languageEnglish
Pages (from-to)227-243
Number of pages17
JournalJournal of Multivariate Analysis
Volume67
Issue number2
DOIs
StatePublished - Nov 1998

Keywords

  • Mean location; degenerate normal distribution; sample Weingarten mapping; cut-locus; Stiefel manifold; test; confidence interval; asymptotic; acceptance-rejection method; simulation

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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