fdWasserstein-package {fdWasserstein}

Application of Optimal Transport to Functional Data Analysis

Description

A package containing functions developed to support statistical analysis on functional covariance operators. In particular,

• Function dwasserstein computes the Wasserstein-Procrustes distance between two covariances.

• Function gaussBary computes the Frechet mean of K covariances with respect to the Procrustes metrics (equivalently, the Wasserstein barycenter of centered Gaussian processes with corresponding covariances) via steepest gradient descent. See Masarotto, Panaretos & Zemel (2019).

• Function tangentPCA performs the tangent space principal component analysis considered in Masarotto, Panaretos & Zemel (2022).

• Function wassersteinTest lets to test the null hypothesis that K covariances are equal using the methodology suggested by Masarotto, Panaretos & Zemel (2022).

• Function wassersteinCluster implements the soft partion procedure proposed by Masarotto & Masarotto (2023).

Author(s)

Valentina Masarotto [aut, cph, cre], Guido Masarotto [aut, cph]

Maintainer: Valentina Masarotto <[e-mail]>

References

Masarotto, V., Panaretos, V.M. & Zemel, Y. (2019) "Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes", Sankhya A 81, 172-213 doi:10.1007/s13171-018-0130-1

Masarotto, V., Panaretos, V.M. & Zemel, Y. (2022) "Transportation-Based Functional ANOVA and PCA for Covariance Operators", arXiv, https://arxiv.org/abs/2212.04797

Masarotto, V. & Masarotto, G. (2023) "Covariance-based soft clustering of functional data based on the Wasserstein-Procrustes metric", Scandinavian Journal of Statistics, doi:10.1111/sjos.12692.