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 |
| Published: |
2016
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| Summary: | 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. |
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