Empirical likelihood in Euclidean and some non-Euclidean spaces
Empirical likelihood is a non-parametric approach to statistical inference which bears some resemblance to parametric approaches and yet avoids making parametric assumptions. The aim of this thesis is to develop theoretical and computational aspects of empirical likelihood when applied to data from...
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
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2020
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| Online Access: | https://eprints.nottingham.ac.uk/59820/ |
| _version_ | 1848799680772702208 |
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| author | Yan, Xi |
| author_facet | Yan, Xi |
| author_sort | Yan, Xi |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Empirical likelihood is a non-parametric approach to statistical inference which bears some resemblance to parametric approaches and yet avoids making parametric assumptions. The aim of this thesis is to develop theoretical and computational aspects of empirical likelihood when applied to data from two different types of non-Euclidean space. The two spaces we focus on are the sphere, which is an important example of a manifold with non-Euclidean structure and is the appropriate sample space in directional statistics; and the 3-Spider, which is an example of a stratified manifold. The focus is mainly on developing empirical likelihood for a Fréchet mean in these two settings. Key achievements are: to prove versions of Wilks’ theorem which open the way to the application of methods of inference including the construction of confidence regions and hypothesis testing; and the development of algorithms for performing the computations. |
| first_indexed | 2025-11-14T20:39:31Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-59820 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:39:31Z |
| publishDate | 2020 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-598202025-02-28T14:46:34Z https://eprints.nottingham.ac.uk/59820/ Empirical likelihood in Euclidean and some non-Euclidean spaces Yan, Xi Empirical likelihood is a non-parametric approach to statistical inference which bears some resemblance to parametric approaches and yet avoids making parametric assumptions. The aim of this thesis is to develop theoretical and computational aspects of empirical likelihood when applied to data from two different types of non-Euclidean space. The two spaces we focus on are the sphere, which is an important example of a manifold with non-Euclidean structure and is the appropriate sample space in directional statistics; and the 3-Spider, which is an example of a stratified manifold. The focus is mainly on developing empirical likelihood for a Fréchet mean in these two settings. Key achievements are: to prove versions of Wilks’ theorem which open the way to the application of methods of inference including the construction of confidence regions and hypothesis testing; and the development of algorithms for performing the computations. 2020-07-15 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/59820/1/PhD%20Final%20Thesis-Empirical%20Likelihood%20in%20Euclidean%20and%20Some%20Non-Euclidean%20Spaces-Charles%20Xi%20Yan%20.pdf Yan, Xi (2020) Empirical likelihood in Euclidean and some non-Euclidean spaces. PhD thesis, University of Nottingham. Empirical Likelihood; Wilks' Theorem for Empirical Likelihood; Local Alternatives; Concavity; Directional Data; Sphere; Fréchet Mean; 3-Spider; Phylogenetic Tree Data; Confidence Region |
| spellingShingle | Empirical Likelihood; Wilks' Theorem for Empirical Likelihood; Local Alternatives; Concavity; Directional Data; Sphere; Fréchet Mean; 3-Spider; Phylogenetic Tree Data; Confidence Region Yan, Xi Empirical likelihood in Euclidean and some non-Euclidean spaces |
| title | Empirical likelihood in Euclidean and some non-Euclidean spaces |
| title_full | Empirical likelihood in Euclidean and some non-Euclidean spaces |
| title_fullStr | Empirical likelihood in Euclidean and some non-Euclidean spaces |
| title_full_unstemmed | Empirical likelihood in Euclidean and some non-Euclidean spaces |
| title_short | Empirical likelihood in Euclidean and some non-Euclidean spaces |
| title_sort | empirical likelihood in euclidean and some non-euclidean spaces |
| topic | Empirical Likelihood; Wilks' Theorem for Empirical Likelihood; Local Alternatives; Concavity; Directional Data; Sphere; Fréchet Mean; 3-Spider; Phylogenetic Tree Data; Confidence Region |
| url | https://eprints.nottingham.ac.uk/59820/ |