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Contributions to the theory of generalized inverses, the linear model and outliers
Column-space conditions are shown to be at the heart of a number of identities linking generalized inverses of rectangular matrices. These identities give some new insights into reparametrizations of the general linear model, and into the imposition of constraints, when the variance-covariance struc...
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| Format: | Thesis |
| Language: | English |
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Department of Statistical Sciences
2015
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| _version_ | 1867613270990389248 |
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| access_status_str | Open Access |
| author | Dunne, Timothy Terence |
| author2 | Troskie, Casper G |
| author_browse | Dunne, Timothy Terence Troskie, Casper G |
| author_facet | Troskie, Casper G Dunne, Timothy Terence |
| author_sort | Dunne, Timothy Terence |
| collection | Thesis |
| description | Column-space conditions are shown to be at the heart of a number of identities linking generalized inverses of rectangular matrices. These identities give some new insights into reparametrizations of the general linear model, and into the imposition of constraints, when the variance-covariance structure is σ².I. Hypothesis-test statistics for non-estimable functions are shown to give no further information than underlying estimable functions. For an arbitrary variance-covariance structure the "sweep-out" method is generalized. The John and Draper model for outliers is extended, and distributional results established. Some diagnostic statistics for outlying or influential observations are considered. A Bayesian formulation of outliers in the general linear model is attempted. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/15668 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:33:28.738Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2015 |
| publishDateRange | 2015 |
| publishDateSort | 2015 |
| publisher | Department of Statistical Sciences |
| publisherStr | Department of Statistical Sciences |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/15668 Contributions to the theory of generalized inverses, the linear model and outliers Dunne, Timothy Terence Troskie, Casper G Mathematical Statistics Column-space conditions are shown to be at the heart of a number of identities linking generalized inverses of rectangular matrices. These identities give some new insights into reparametrizations of the general linear model, and into the imposition of constraints, when the variance-covariance structure is σ².I. Hypothesis-test statistics for non-estimable functions are shown to give no further information than underlying estimable functions. For an arbitrary variance-covariance structure the "sweep-out" method is generalized. The John and Draper model for outliers is extended, and distributional results established. Some diagnostic statistics for outlying or influential observations are considered. A Bayesian formulation of outliers in the general linear model is attempted. 2015-12-08T06:57:06Z 2015-12-08T06:57:06Z 1982 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/15668 eng application/pdf Department of Statistical Sciences Faculty of Science University of Cape Town |
| spellingShingle | Mathematical Statistics Dunne, Timothy Terence Contributions to the theory of generalized inverses, the linear model and outliers |
| thesis_degree_str | Doctoral |
| title | Contributions to the theory of generalized inverses, the linear model and outliers |
| title_full | Contributions to the theory of generalized inverses, the linear model and outliers |
| title_fullStr | Contributions to the theory of generalized inverses, the linear model and outliers |
| title_full_unstemmed | Contributions to the theory of generalized inverses, the linear model and outliers |
| title_short | Contributions to the theory of generalized inverses, the linear model and outliers |
| title_sort | contributions to the theory of generalized inverses the linear model and outliers |
| topic | Mathematical Statistics |
| url | http://hdl.handle.net/11427/15668 |
| work_keys_str_mv | AT dunnetimothyterence contributionstothetheoryofgeneralizedinversesthelinearmodelandoutliers |