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
and two methods for 2-sample tests for equality assuming
Gaussian data in
For supervised and unsupervised learning,
it contains a method to classify functional data with
respect to each category's covariance operator in
and it contains a method to cluster functional data,
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
fda package and its functional basis representations
of the data.
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):409–422.
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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