Asymptotic behavior of sample mean location for manifolds

DOI10.1016/0167-7152(95)00007-0zbMath0848.62017OpenAlexW1978040199MaRDI QIDQ1914300

Harrie Hendriks, Zinoviy Landsman

Publication date: 27 October 1996

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-7152(95)00007-0

zbMATH Keywords

submanifoldschi-squared distributioncut-locusWeingarten mappingsample mean locationdegenerate normal distributionasymptotic least-squares statistics inferencecompact smooth submanifolds of Euclidean spaceempirical mean location

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Asymptotic properties of nonparametric inference (62G20) Local differential geometry (53B99) Classical differential geometry (53A99)

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On the meaning of mean shape: manifold stability, locus and the two sample test ⋮ Sticky central limit theorems on open books ⋮ A comment to ``Statistics on manifolds and landmark based image analysis: a nonparametric theory with applications ⋮ Some properties of a Cauchy family on the sphere derived from the Möbius transformations ⋮ Intrinsic inference on the mean geodesic of planar shapes and tree discrimination by leaf growth ⋮ On the CLT on Low Dimensional Stratified Spaces ⋮ Asymptotic data analysis on manifolds ⋮ On means and their asymptotics: circles and shape spaces ⋮ Backward nested descriptors asymptotics with inference on stem cell differentiation ⋮ Mean location and sample mean location on manifolds: Asymptotics, tests, confidence regions ⋮ The Extrinsic Geometry of Dynamical Systems Tracking Nonlinear Matrix Projections

Cites Work

• A Cramér-Rao type lower bound for estimators with values in a manifold
• Sur le cut-locus d'une variété plongee
• Bounds on Moments of Certain Random Variables
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