Principal component analysis for functional data on Riemannian manifolds and spheres

DOI10.1214/17-AOS1660zbMath1454.62553arXiv1705.06226WikidataQ115240835 ScholiaQ115240835MaRDI QIDQ1990583

Xiongtao Dai, Hans-Georg Müller

Publication date: 25 October 2018

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

Full work available at URL: https://arxiv.org/abs/1705.06226

zbMATH Keywords

uniform convergenceRiemannian manifolddimension reductioncentral limit theoremtrajectorycompositional datafunctional data analysisfunctional principal component analysisprincipal geodesic analysis

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Asymptotic properties of nonparametric inference (62G20) Functional data analysis (62R10) Statistics on manifolds (62R30) Nonparametric estimation (62G05)

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Uses Software

• fda (R)

Cites Work

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• Nonlinear manifold representations for functional data
• Smooth principal component analysis over two-dimensional manifolds with an application to neuroimaging
• Central limit theorems for C(S)-valued random variables
• Large sample theory of intrinsic and extrinsic sample means on manifolds. I
• Linear processes in function spaces. Theory and applications
• Backward nested descriptors asymptotics with inference on stem cell differentiation
• Weak convergence and empirical processes. With applications to statistics
• Statistical analysis of trajectories on Riemannian manifolds: bird migration, hurricane tracking and video surveillance
• Functional data analysis.
• Large sample theory of intrinsic and extrinsic sample means on manifolds. II.
• Nonparametric Statistics on Manifolds and Their Applications to Object Data Analysis
• Omnibus CLTs for Fréchet means and nonparametric inference on non-Euclidean spaces
• Analysis of principal nested spheres
• Multivariate functional principal component analysis: A normalization approach
• Simplex Mixed‐Effects Models for Longitudinal Proportional Data
• Statistical Analysis of Spherical Data
• Inference for Density Families Using Functional Principal Component Analysis
• Fitting Smooth Paths to Speherical Data
• Principal Modes of Variation for Processes with Continuous Sample Curves
• Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators
• Regression Models on Riemannian Symmetric Spaces
• Multiscale Representations for Manifold-Valued Data
• Functional data analysis for density functions by transformation to a Hilbert space