Intrinsic Riemannian functional data analysis
From MaRDI portal
Publication:2284383
DOI10.1214/18-AOS1787zbMath1435.62264arXiv1812.01831OpenAlexW3105336892WikidataQ115240831 ScholiaQ115240831MaRDI QIDQ2284383
Publication date: 15 January 2020
Published in: The Annals of Statistics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1812.01831
parallel transportfunctional linear regressionfunctional principal componenttensor Hilbert spaceintrinsic Riemannian Karhunen-Loève expansion
Factor analysis and principal components; correspondence analysis (62H25) Functional data analysis (62R10) Statistics on manifolds (62R30) Linear regression; mixed models (62J05) Applications of statistics to biology and medical sciences; meta analysis (62P10)
Related Items
Intrinsic Hölder classes of density functions on Riemannian manifolds and lower bounds to convergence rates, Sliced Inverse Regression in Metric Spaces, Statistical inference on the Hilbert sphere with application to random densities, Estimation and Model Selection for Nonparametric Function-on-Function Regression, Intrinsic Riemannian functional data analysis for sparse longitudinal observations, Discussion of “LESA: Longitudinal Elastic Shape Analysis of Brain Subcortical Structures”, Wasserstein Regression, Modeling sparse longitudinal data on Riemannian manifolds, Wasserstein gradients for the temporal evolution of probability distributions, Additive regression for non-Euclidean responses and predictors, A new RKHS-based global testing for functional linear model, Feature extraction for functional time series: theory and application to NIR spectroscopy data, Amplitude mean of functional data on \(\mathbb{S}^2\) and its accurate computation, Nonparametric regression on Lie groups with measurement errors
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Functional linear regression analysis for longitudinal data
- Fréchet regression for random objects with Euclidean predictors
- From sparse to dense functional data and beyond
- Nonlinear manifold representations for functional data
- Smooth principal component analysis over two-dimensional manifolds with an application to neuroimaging
- A reproducing kernel Hilbert space approach to functional linear regression
- Limit theorems for empirical Fréchet means of independent and non-identically distributed manifold-valued random variables
- On the differential geometry of tangent bundles of Riemannian manifolds
- Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference
- Nonparametric methods for inference in the presence of instrumental variables
- CLT in functional linear regression models
- Riemannian geometry for the statistical analysis of diffusion tensor data
- Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging
- Methodology and convergence rates for functional linear regression
- Large sample theory of intrinsic and extrinsic sample means on manifolds. I
- Linear processes in function spaces. Theory and applications
- Smoothed functional principal components analysis by choice of norm
- Principal component analysis for functional data on Riemannian manifolds and spheres
- Object oriented data analysis: sets of trees
- Functional data analysis.
- Nonparametric functional data analysis. Theory and practice.
- Estimation and detection theory for multiple stochastic processes
- Partially functional linear regression in high dimensions
- Recursive Computation of the Fréchet Mean on Non-positively Curved Riemannian Manifolds with Applications
- Introduction to Smooth Manifolds
- Riemannian $L^{p}$ center of mass: Existence, uniqueness, and convexity
- Some Statistical Methods for Comparison of Growth Curves
- A Representation of Vector-Valued Random Processes
- A Characterisation of Hilbert Space Using the Central Limit Theorem
- Introduction to Functional Data Analysis
- Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains
- Principal components of random variables with values in a seperable hilbert space
- Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators
- A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
- Regression Models on Riemannian Symmetric Spaces
- On Properties of Functional Principal Components Analysis
- Geometric Means in a Novel Vector Space Structure on Symmetric Positive‐Definite Matrices
- Local polynomial regression for symmetric positive definite matrices
- Nonparametric Regression between General Riemannian Manifolds
- Functional Data Analysis for Sparse Longitudinal Data