Second order proximal methods applied to elastic net penalised vector generalised linear models
The Vector Generalised Linear Model (VGLM) framework extends Generalised Linear Models (GLMs) to a large number of univariate and multivariate statistical models. The object of this thesis is to study the estimation of the maximum elastic net penalised log-likelihood of VGLM models. As the elastic n...
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Format: | Thesis |
Language: | English |
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2016
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author | Nortier, B |
author2 | Doucet, A |
author_facet | Doucet, A Nortier, B |
author_sort | Nortier, B |
collection | OXFORD |
description | The Vector Generalised Linear Model (VGLM) framework extends Generalised Linear Models (GLMs) to a large number of univariate and multivariate statistical models. The object of this thesis is to study the estimation of the maximum elastic net penalised log-likelihood of VGLM models. As the elastic net penalty has a separable non-differentiable part, second-order proximal methods are considered. For VGLMs, depending on the model, it may be more convenient to use the Fisher information matrix instead of the Hessian. Hence, we propose a proximal Fisher scoring method. Two examples are then investigated. The first example is an application of an elastic net penalised ordinal probit model to the prediction of mid-market price changes for tick-by-tick Limit Order Book data. The second example is an application of an Expectation Maximisation (EM) proximal Newton/Fisher scoring algorithm to variable selection for a bivariate Poisson regression model applied to health care data. |
first_indexed | 2024-03-06T21:57:01Z |
format | Thesis |
id | oxford-uuid:4d41dc36-4c62-4911-8eef-97e4e2bcd59d |
institution | University of Oxford |
language | English |
last_indexed | 2024-03-06T21:57:01Z |
publishDate | 2016 |
record_format | dspace |
spelling | oxford-uuid:4d41dc36-4c62-4911-8eef-97e4e2bcd59d2022-03-26T15:54:30ZSecond order proximal methods applied to elastic net penalised vector generalised linear modelsThesishttp://purl.org/coar/resource_type/c_bdccuuid:4d41dc36-4c62-4911-8eef-97e4e2bcd59dEnglishORA Deposit2016Nortier, BDoucet, AThe Vector Generalised Linear Model (VGLM) framework extends Generalised Linear Models (GLMs) to a large number of univariate and multivariate statistical models. The object of this thesis is to study the estimation of the maximum elastic net penalised log-likelihood of VGLM models. As the elastic net penalty has a separable non-differentiable part, second-order proximal methods are considered. For VGLMs, depending on the model, it may be more convenient to use the Fisher information matrix instead of the Hessian. Hence, we propose a proximal Fisher scoring method. Two examples are then investigated. The first example is an application of an elastic net penalised ordinal probit model to the prediction of mid-market price changes for tick-by-tick Limit Order Book data. The second example is an application of an Expectation Maximisation (EM) proximal Newton/Fisher scoring algorithm to variable selection for a bivariate Poisson regression model applied to health care data. |
spellingShingle | Nortier, B Second order proximal methods applied to elastic net penalised vector generalised linear models |
title | Second order proximal methods applied to elastic net penalised vector generalised linear models |
title_full | Second order proximal methods applied to elastic net penalised vector generalised linear models |
title_fullStr | Second order proximal methods applied to elastic net penalised vector generalised linear models |
title_full_unstemmed | Second order proximal methods applied to elastic net penalised vector generalised linear models |
title_short | Second order proximal methods applied to elastic net penalised vector generalised linear models |
title_sort | second order proximal methods applied to elastic net penalised vector generalised linear models |
work_keys_str_mv | AT nortierb secondorderproximalmethodsappliedtoelasticnetpenalisedvectorgeneralisedlinearmodels |