fdcov-package: Analysis of Covariance Operators.
In fdcov: Analysis of Covariance Operators

Description Details Author(s) References See Also

fdcov a variety of tools for the analysis of covariance operators including k-sample tests for equality and classification and clustering methods.

This package contains a collection of tools for performing statistical inference on functional data specifically through an analysis of the covariance structure of the data. It includes two methods for performing a k-sample test for equality of covariance in ksample.perm and ksample.com and two methods for 2-sample tests for equality assuming Gaussian data in ksample.gauss and ksample.vstab. For supervised and unsupervised learning, it contains a method to classify functional data with respect to each category's covariance operator in classif.com, and it contains a method to cluster functional data, cluster.com, again based on the covariance structure of the data.

The current version of this package assumes that all functional data is sampled on the same grid at the same intervals. Future updates are planned to allow for the below methods to interface with the fda package and its functional basis representations of the data.

Alessandra Cabassi alessandra.cabassi@mail.polimi.it, Adam B Kashlak kashlak@ualberta.ca

Cabassi, A., Pigoli, D., Secchi, P., Carter, P. A. (2017). Permutation tests for the equality of covariance operators of functional data with applications to evolutionary biology. Electron. J. Statist. 11(2), pp.3815–3840.

Kashlak, Adam B, John AD Aston, and Richard Nickl (2016). "Inference on covariance operators via concentration inequalities: k-sample tests, classification, and clustering via Rademacher complexities", April, 2016 (in review)

Pigoli, Davide, John AD Aston, Ian L Dryden, and Piercesare Secchi. "Distances and inference for covariance operators." Biometrika (2014): 101(2):409<e2><80><93>422.

Panaretos, Victor M., David Kraus, and John H. Maddocks. "Second-order comparison of Gaussian random functions and the geometry of DNA minicircles." Journal of the American Statistical Association 105.490 (2010): 670-682.

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