Confidence sets for model selection

Diplôme Thèse Confidence sets for model selection eng 2016-08-15 author Hannay Mark 811728 director Ronchetti Elvezio 0000-0003-2231-4556 22756 10.13097/archive-ouverte/unige:86467 urn:nbn:ch:unige-864673 GSEM 31 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. Model selection Confidence set Uncertainty in model selection Relevance and irrelevance testing Dewey 310 117 Research Center for Statistics S5 false 18810671-300f-485e-b448-845feae587b8 Thesis Public PHD-THESIS.pdf 1287348 application/pdf openAccess Faculté d'économie et de management / Research Center for Statistics

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Hannay, Mark