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Confidence sets for model selection

Defense Thèse de doctorat : Univ. Genève, 2016 - GSEM 31 - 2016/08/15
Abstract At first glance the goals of model selection might seem clear. Out of a set of possible models, we want to select the ”best” or a subset of ”best” models. This notion of ”best” however is not well defined, since it obviously depends on the initial goals of the selection. In order to study the uncertainty in model selection, we introduce a new definition of a model, where the models are no longer defined through zero and non-zero components but through irrelevant and relevant component. Then inspired by confidence intervals for estimated parameters, we propose a method to build confidence sets for model selection in a parametric setting, i.e. create sets of models within which the true model is included with a certain confidence. This allows us to perform inference on model selection. We discuss the computational challenges with such a method, how to find p-values (for the model), consistency in model selection and through a data set and a simulation study show the implications of this new method.
Keywords Model selectionConfidence setUncertainty in model selectionRelevance and irrelevance testing
URN: urn:nbn:ch:unige-864673
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HANNAY, Mark. Confidence sets for model selection. Université de Genève. Thèse, 2016. doi: 10.13097/archive-ouverte/unige:86467 https://archive-ouverte.unige.ch/unige:86467

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Deposited on : 2016-08-29

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