Transportation-based functional ANOVA and PCA for covariance operators

Victor M. Panaretos, Valentina Masarotto, Yoav Zemel

Publication date: 29 May 2024

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

trace-class operator coupling Gaussian measure functional data analysis optimal transport Fréchet mean procrustes analysis tangent space PCA multimarginal transport

Mathematics Subject Classification ID

Gaussian processes (60G15) Functional data analysis (62R10) Random operators and equations (aspects of stochastic analysis) (60H25) Analysis of variance and covariance (ANOVA) (62J10)

Cites Work

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A simple multiway ANOVA for functional data
Equivalence and perpendicularity of Gaussian processes
A comparison of tests for the one-way ANOVA problem for functional data
Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging
Common functional principal components
Testing equality between several populations covariance operators
Fréchet means and Procrustes analysis in Wasserstein space
Penalized discriminant analysis
Smoothed functional principal components analysis by choice of norm
Functional principal components analysis by choice of norm
Functional ANOVA based on empirical characteristic functionals
Inference on covariance operators via concentration inequalities: $k$-sample tests, classification, and clustering via Rademacher complexities
Permutation tests for the equality of covariance operators of functional data with applications to evolutionary biology
Functional data analysis.
Nonparametric functional data analysis. Theory and practice.
Distances and inference for covariance operators
Dispersion operators and resistant second-order functional data analysis
Testing the Equality of Covariance Operators in Functional Samples
The permutation testing approach: a review
Stochastic Equations in Infinite Dimensions
Second-Order Comparison of Gaussian Random Functions and the Geometry of DNA Minicircles
Bootstrap-based testing of equality of mean functions or equality of covariance operators for functional data
Distance‐Based Tests for Homogeneity of Multivariate Dispersions
Admissible Bayes Character of $T^2-, R^2-$, and Other Fully Invariant Tests for Classical Multivariate Normal Problems
On Majorization, Factorization, and Range Inclusion of Operators on Hilbert Space
On Tests of the Equality of Two Covariance Matrices
Achieving near Perfect Classification for Functional Data
Functional Data Analysis for Sparse Longitudinal Data
On a Heuristic Method of Test Construction and its use in Multivariate Analysis
The statistical analysis of acoustic phonetic data: exploring differences between spoken Romance languages

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