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Semi-parametric mixtures of quantile regressions
Mini Dissertation (MSc (Advanced Data Analytics))--University of Pretoria, 2023.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2023
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| _version_ | 1867613526105784320 |
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| access_status_str | Open Access |
| author2 | Millard, Sollie M. |
| author_browse | Millard, Sollie M. |
| author_facet | Millard, Sollie M. |
| collection | Thesis |
| dc_rights_str_mv | © 2022 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Mini Dissertation (MSc (Advanced Data Analytics))--University of Pretoria, 2023. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/90183 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:37:32.711Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2023 |
| publishDateRange | 2023 |
| publishDateSort | 2023 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/90183 Semi-parametric mixtures of quantile regressions Millard, Sollie M. gouwsdivan@gmail.com Kanfer, F.H.J. (Frans) Gouws, Divan UCTD Mixture regression Quantile regression Semi-parametric model Expectation-maximisation Kernel methods Mini Dissertation (MSc (Advanced Data Analytics))--University of Pretoria, 2023. Mixtures of quantile regressions are explored through the lens of a kernel density based EM-type algorithm and a newly proposed CEM-type algorithm. This allows the simultaneous clustering and modeling of conditional quantiles without the need to assume symmetric or identical error distributions for any of the components. We conduct simulation studies and apply both algorithms to real life datasets. The first has already been investigated by fitting the EM-type algorithm and we show that the CEM-type algorithm produces similar results. The second is a homoscedastic dataset which has been explored through the lens of univariate quantile regression. We begin by modeling the mixtures of the conditional medians as a robust alternative to mixtures of conditional means. Mixtures of other conditional quantiles are modeled as well to get a more complete understanding of the conditional distribution. This, however, proves to be a challenging task for datasets which are not easily separable and may lead to unsatisfactory results, especially when considering low quantiles or high quantiles such as 0.1 or 0.9 respectively. The theory of the EM-type algorithm is provided in detail and the proposed CEM-type algorithm is shown to provide a substantial improvement in the model convergence speed, but often at the cost of increased bias in the parameter estimates. We conclude with a discussion of some of the limitations and areas for future research. Statistics MSc (Advanced Data Analytics) Unrestricted 2023-03-23T07:00:27Z 2023-03-23T07:00:27Z 2023 2023 Mini Dissertation * S2023 http://hdl.handle.net/2263/90183 en © 2022 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | UCTD Mixture regression Quantile regression Semi-parametric model Expectation-maximisation Kernel methods Semi-parametric mixtures of quantile regressions |
| title | Semi-parametric mixtures of quantile regressions |
| title_full | Semi-parametric mixtures of quantile regressions |
| title_fullStr | Semi-parametric mixtures of quantile regressions |
| title_full_unstemmed | Semi-parametric mixtures of quantile regressions |
| title_short | Semi-parametric mixtures of quantile regressions |
| title_sort | semi parametric mixtures of quantile regressions |
| topic | UCTD Mixture regression Quantile regression Semi-parametric model Expectation-maximisation Kernel methods |
| url | http://hdl.handle.net/2263/90183 |