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Focussed Information Criteria for Model Selection and Model Averaging

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The traditional approaches to model selection, e.g. those based on the Akaike and Bayesian information criteria (AIC and BIC ), work in “overall modus”, without considering what the selected model actually may be used for later in the inference process. I shall discuss various versions of focussed information criteria (FIC) for different types of situations, where the operating idea is to take explicitly on board what the focus of the analysis is. Thus I decide to not see it as particularly contradictory that one model may be best for analysing say the mean structure whereas another model may be better for analysing say the skewness structure (with the same set of data and the same list of candidate models). I will first review the basic FIC machinery developed in joint earlier work with Gerda Claeskens (cf. several JASA papers and our 2008 CUP book) for the case of comparing (and averaging over) a class of parametric candidate models and then present some ongoing work with one of my Oslo students, pertaining to FIC comparisons between parametric and nonparametric models. Such problems are of a different character in that one needs to compare models with likelihoods with models without likelihoods.

This talk is part of the Statistics series.

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