Distances and inference for covariance operators

A framework is developed for inference concerning the covariance operator of a functional random process, where the covariance operator itself is an object of interest for statistical analysis. Distances for comparing positive-definite covariance matrices are either extended or shown to be inapplica...

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Main Authors:	Pigoli, Davide, Aston, John A.D., Dryden, Ian L., Secchi, Piercesare
Format:	Article
Language:	English
Published:	Oxford University Press 2014
Online Access:	http://eprints.nottingham.ac.uk/41017/ http://eprints.nottingham.ac.uk/41017/ http://eprints.nottingham.ac.uk/41017/ http://eprints.nottingham.ac.uk/41017/1/Pigolietal2014-asu008.pdf

id	nottingham-41017
recordtype	eprints
spelling	nottingham-410172017-10-13T01:34:41Z http://eprints.nottingham.ac.uk/41017/ Distances and inference for covariance operators Pigoli, Davide Aston, John A.D. Dryden, Ian L. Secchi, Piercesare A framework is developed for inference concerning the covariance operator of a functional random process, where the covariance operator itself is an object of interest for statistical analysis. Distances for comparing positive-definite covariance matrices are either extended or shown to be inapplicable to functional data. In particular, an infinite-dimensional analogue of the Procrustes size-and-shape distance is developed. Convergence of finite-dimensional approximations to the infinite-dimensional distance metrics is also shown. For inference, a Fréchet estimator of both the covariance operator itself and the average covariance operator is introduced. A permutation procedure to test the equality of the covariance operators between two groups is also considered. Additionally, the use of such distances for extrapolation to make predictions is explored. As an example of the proposed methodology, the use of covariance operators has been suggested in a philological study of cross-linguistic dependence as a way to incorporate quantitative phonetic information. It is shown that distances between languages derived from phonetic covariance functions can provide insight into the relationships between the Romance languages. Oxford University Press 2014-04-17 Article PeerReviewed application/pdf en cc_by http://eprints.nottingham.ac.uk/41017/1/Pigolietal2014-asu008.pdf Pigoli, Davide and Aston, John A.D. and Dryden, Ian L. and Secchi, Piercesare (2014) Distances and inference for covariance operators. Biometrika, 101 (2). pp. 409-422. ISSN 1464-3510 https://academic.oup.com/biomet/article-lookup/doi/10.1093/biomet/asu008 doi:10.1093/biomet/asu008 doi:10.1093/biomet/asu008
repository_type	Digital Repository
institution_category	Local University
institution	University of Nottingham Malaysia Campus
building	Nottingham Research Data Repository
collection	Online Access
language	English
description	A framework is developed for inference concerning the covariance operator of a functional random process, where the covariance operator itself is an object of interest for statistical analysis. Distances for comparing positive-definite covariance matrices are either extended or shown to be inapplicable to functional data. In particular, an infinite-dimensional analogue of the Procrustes size-and-shape distance is developed. Convergence of finite-dimensional approximations to the infinite-dimensional distance metrics is also shown. For inference, a Fréchet estimator of both the covariance operator itself and the average covariance operator is introduced. A permutation procedure to test the equality of the covariance operators between two groups is also considered. Additionally, the use of such distances for extrapolation to make predictions is explored. As an example of the proposed methodology, the use of covariance operators has been suggested in a philological study of cross-linguistic dependence as a way to incorporate quantitative phonetic information. It is shown that distances between languages derived from phonetic covariance functions can provide insight into the relationships between the Romance languages.
format	Article
author	Pigoli, Davide Aston, John A.D. Dryden, Ian L. Secchi, Piercesare
spellingShingle	Pigoli, Davide Aston, John A.D. Dryden, Ian L. Secchi, Piercesare Distances and inference for covariance operators
author_facet	Pigoli, Davide Aston, John A.D. Dryden, Ian L. Secchi, Piercesare
author_sort	Pigoli, Davide
title	Distances and inference for covariance operators
title_short	Distances and inference for covariance operators
title_full	Distances and inference for covariance operators
title_fullStr	Distances and inference for covariance operators
title_full_unstemmed	Distances and inference for covariance operators
title_sort	distances and inference for covariance operators
publisher	Oxford University Press
publishDate	2014
url	http://eprints.nottingham.ac.uk/41017/ http://eprints.nottingham.ac.uk/41017/ http://eprints.nottingham.ac.uk/41017/ http://eprints.nottingham.ac.uk/41017/1/Pigolietal2014-asu008.pdf
first_indexed	2018-09-06T13:10:10Z
last_indexed	2018-09-06T13:10:10Z
_version_	1610863776658096128

Distances and inference for covariance operators

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