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...
| Main Authors: | , , , |
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| Format: | Article |
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Oxford University Press
2014
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| Online Access: | https://eprints.nottingham.ac.uk/41017/ |
| _version_ | 1848796179194707968 |
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| author | Pigoli, Davide Aston, John A.D. Dryden, Ian L. Secchi, Piercesare |
| author_facet | Pigoli, Davide Aston, John A.D. Dryden, Ian L. Secchi, Piercesare |
| author_sort | Pigoli, Davide |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-14T19:43:52Z |
| format | Article |
| id | nottingham-41017 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:52Z |
| publishDate | 2014 |
| publisher | Oxford University Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-410172020-05-04T16:46:34Z https://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 Pigoli, Davide, Aston, John A.D., Dryden, Ian L. and Secchi, Piercesare (2014) Distances and inference for covariance operators. Biometrika, 101 (2). pp. 409-422. ISSN 1464-3510 Distance metric; Functional data analysis; Procrustes analysis; Shape analysis https://academic.oup.com/biomet/article-lookup/doi/10.1093/biomet/asu008 doi:10.1093/biomet/asu008 doi:10.1093/biomet/asu008 |
| spellingShingle | Distance metric; Functional data analysis; Procrustes analysis; Shape analysis Pigoli, Davide Aston, John A.D. Dryden, Ian L. Secchi, Piercesare Distances and inference for covariance operators |
| title | 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_short | Distances and inference for covariance operators |
| title_sort | distances and inference for covariance operators |
| topic | Distance metric; Functional data analysis; Procrustes analysis; Shape analysis |
| url | https://eprints.nottingham.ac.uk/41017/ https://eprints.nottingham.ac.uk/41017/ https://eprints.nottingham.ac.uk/41017/ |