Asymptotic data analysis on manifolds

DOI10.1214/009053606000000993zbMath1114.62064arXiv0708.0474OpenAlexW2092176948MaRDI QIDQ997373

Harrie Hendriks, Zinoviy Landsman

Publication date: 23 July 2007

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0708.0474

zbMATH Keywords

stabilizationconfidence regionsphereStiefel manifoldspatial medianspherical distributioncutlocuscompact submanifold of Euclidean spacemean locationmedian locationmultivariate Lindeberg conditionWeingarten mapping

Mathematics Subject Classification ID

Directional data; spatial statistics (62H11) Asymptotic properties of nonparametric inference (62G20) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Nonparametric tolerance and confidence regions (62G15) Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Classical differential geometry (53A99)

Related Items (7)

A universal, canonical dispersive ordering in metric spaces ⋮ Partly linear models on Riemannian manifolds ⋮ The location of a minimum variance squared distance functional ⋮ Rates of the strong uniform consistency for the kernel-type regression function estimators with general kernels on manifolds ⋮ Minimization of the root of a quadratic functional under a system of affine equality constraints with application to portfolio management ⋮ Kernel density estimation on Riemannian manifolds: asymptotic results ⋮ Level set and density estimation on manifolds

Cites Work

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• Uniqueness of the spatial median
• Asymptotic behavior of sample mean direction for spheres
• Multivariate location estimation using extension of \(R\)-estimates through \(U\)-statistics type approach
• Mean location and sample mean location on manifolds: Asymptotics, tests, confidence regions
• Large sample theory of intrinsic and extrinsic sample means on manifolds. I
• Nonparametric comparison of mean directions or mean axes
• Asymptotic behavior of sample mean location for manifolds
• Central limit theorems revisited
• Spatial median and directional data
• Morse Theory. (AM-51)
• The multivariate L ₁ -median and associated data depth
• Chance and Stability

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