Robust versions of classical multivariate techniques based on the Cauchy likelihood
Classical multivariate analysis techniques such as principal components analysis (PCA), canonical correlation analysis (CCA) and discriminant analysis (DA) can be badly affected when extreme outliers are present. The purpose of this thesis is to present new robust versions of these methods. Our appr...
| Main Author: | |
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
| Published: |
2013
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| Online Access: | https://eprints.nottingham.ac.uk/13446/ |
| _version_ | 1848791735344300032 |
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| author | Fayomi, Aisha Fouad |
| author_facet | Fayomi, Aisha Fouad |
| author_sort | Fayomi, Aisha Fouad |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Classical multivariate analysis techniques such as principal components analysis (PCA), canonical correlation analysis (CCA) and discriminant analysis (DA) can be badly affected when extreme outliers are present. The purpose of this thesis is to present new robust versions of these methods. Our approach is based on the following observation: the classical approaches to PCA, CCA and DA can all be interpreted as operations on a Gaussian likelihood function. Consequently, PCA, CCA and DA can be robustified by replacing the Gaussian likelihood with a Cauchy likelihood. The performance of the Cauchy version of each of these procedures is studied in detail both theoretically, through calculation of the relevant influence function, and numerically, through numerous examples involving real and simulated data. Our results demonstrate that the new procedures have good robustness properties which are certainly far superior to these of the classical versions. |
| first_indexed | 2025-11-14T18:33:14Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-13446 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T18:33:14Z |
| publishDate | 2013 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-134462025-02-28T11:25:14Z https://eprints.nottingham.ac.uk/13446/ Robust versions of classical multivariate techniques based on the Cauchy likelihood Fayomi, Aisha Fouad Classical multivariate analysis techniques such as principal components analysis (PCA), canonical correlation analysis (CCA) and discriminant analysis (DA) can be badly affected when extreme outliers are present. The purpose of this thesis is to present new robust versions of these methods. Our approach is based on the following observation: the classical approaches to PCA, CCA and DA can all be interpreted as operations on a Gaussian likelihood function. Consequently, PCA, CCA and DA can be robustified by replacing the Gaussian likelihood with a Cauchy likelihood. The performance of the Cauchy version of each of these procedures is studied in detail both theoretically, through calculation of the relevant influence function, and numerically, through numerous examples involving real and simulated data. Our results demonstrate that the new procedures have good robustness properties which are certainly far superior to these of the classical versions. 2013-07-10 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/13446/1/AishaFF_Final_Th_with_R_pdfcode_Sep_updated.pdf Fayomi, Aisha Fouad (2013) Robust versions of classical multivariate techniques based on the Cauchy likelihood. PhD thesis, University of Nottingham. |
| spellingShingle | Fayomi, Aisha Fouad Robust versions of classical multivariate techniques based on the Cauchy likelihood |
| title | Robust versions of classical multivariate techniques based on the Cauchy likelihood |
| title_full | Robust versions of classical multivariate techniques based on the Cauchy likelihood |
| title_fullStr | Robust versions of classical multivariate techniques based on the Cauchy likelihood |
| title_full_unstemmed | Robust versions of classical multivariate techniques based on the Cauchy likelihood |
| title_short | Robust versions of classical multivariate techniques based on the Cauchy likelihood |
| title_sort | robust versions of classical multivariate techniques based on the cauchy likelihood |
| url | https://eprints.nottingham.ac.uk/13446/ |