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Essays on estimation strategies addressing label-switching in Gaussian mixtures of semi- and non-parametric regressions
Thesis (PhD (Mathematical Statistics))--University of Pretoria, 2024.
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University of Pretoria
2024
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| _version_ | 1867613674377576448 |
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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 | © 2023 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 | Thesis (PhD (Mathematical Statistics))--University of Pretoria, 2024. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/96827 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:39:54.193Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| 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:2263/96827 Essays on estimation strategies addressing label-switching in Gaussian mixtures of semi- and non-parametric regressions Millard, Sollie M. spiwe.skhosana@up.ac.za Kanfer, F.H.J. (Frans) Skhosana, Sphiwe Bonakele UCTD Sustainable Development Goals (SDGs) Mixture modelling Label-switching Non-parametric regression Local-likelihood estimation Computational statistics Thesis (PhD (Mathematical Statistics))--University of Pretoria, 2024. Gaussian mixtures of non-parametric regressions (GMNRs) are a flexible class of Gaussian mixtures of regressions (GMRs). These models assume that some or all of the parameters of GMRs are non-parametric functions of the covariates. This flexibility gives these models wide applicability for studying the dependence of one variable on one or more covariates when the underlying population is made up of unobserved subpopulations. The predominant approach used to estimate the GMRs model is maximum likelihood via the Expectation-Maximisation (EM) algorithm. Due to the presence of non-parametric terms in GMNRs, the model estimation poses a computational challenge. A local-likelihood estimation of the non-parametric functions via the EM algorithm may be subject to label-switching. To estimate the non-parametric functions, we have to define a local-likelihood function for each local grid point on the domain of a covariate. If we separately maximise each local-likelihood function, using the EM algorithm, the labels attached to the mixture components may switch from one local grid point to the next. The practical consequence of this label-switching is characterised by non-parametric estimates that are non-smooth, exhibiting irregular behaviour at local points where the switch took place. In this thesis, we propose effective estimation strategies to address label-switching. The common thread that underlies the proposed strategies is the replacement of the separate maximisations of the local-likelihood functions with simultaneous maximisation. The effectiveness of the proposed methods is demonstrated on finite sample data using simulations. Furthermore, the practical usefulness of the proposed methods is demonstrated through applications on real data. Statistics PhD (Mathematical Statistics) Unrestricted Faculty of Economic And Management Sciences 2024-07-05T07:38:30Z 2024-07-05T07:38:30Z 2024-09-30 2024-04-30 Thesis *In this thesis, Essays on estimation strategies addressing label-switching in Gaussian mixtures of semi- and non-parametric regression, the candidate developed new methods to address the label-switching problem when estimating models from a flexible class of Gaussian mixtures of regression models. Using a systematic approach, the candidate developed an objective-based estimation procedure and a model-based estimation procedure. A simulation approach was used to demonstrate the effectiveness of the proposed procedures in addressing label-switching. The practical usefulness of the proposed estimation procedures is demonstrated through applications on real world problem scenarios. This research contributes to our understanding of label-switching in the context of non-parametric likelihood estimation using the EM algorithm. http://hdl.handle.net/2263/96827 DOI: https://doi.org/10.25403/UPresearchdata.26176846.v1 10.25403/UPresearchdata.26176846 en © 2023 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 Sustainable Development Goals (SDGs) Mixture modelling Label-switching Non-parametric regression Local-likelihood estimation Computational statistics Essays on estimation strategies addressing label-switching in Gaussian mixtures of semi- and non-parametric regressions |
| title | Essays on estimation strategies addressing label-switching in Gaussian mixtures of semi- and non-parametric regressions |
| title_full | Essays on estimation strategies addressing label-switching in Gaussian mixtures of semi- and non-parametric regressions |
| title_fullStr | Essays on estimation strategies addressing label-switching in Gaussian mixtures of semi- and non-parametric regressions |
| title_full_unstemmed | Essays on estimation strategies addressing label-switching in Gaussian mixtures of semi- and non-parametric regressions |
| title_short | Essays on estimation strategies addressing label-switching in Gaussian mixtures of semi- and non-parametric regressions |
| title_sort | essays on estimation strategies addressing label switching in gaussian mixtures of semi and non parametric regressions |
| topic | UCTD Sustainable Development Goals (SDGs) Mixture modelling Label-switching Non-parametric regression Local-likelihood estimation Computational statistics |
| url | http://hdl.handle.net/2263/96827 |