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Article

Confidence Distributions for FIC Scores

Department of Mathematics, University of Oslo, P.B. 1053, 0316 Oslo, Norway
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Received: 19 December 2019 / Revised: 21 May 2020 / Accepted: 12 June 2020 / Published: 1 July 2020
(This article belongs to the Special Issue Bayesian and Frequentist Model Averaging)
When using the Focused Information Criterion (FIC) for assessing and ranking candidate models with respect to how well they do for a given estimation task, it is customary to produce a so-called FIC plot. This plot has the different point estimates along the y-axis and the root-FIC scores on the x-axis, these being the estimated root-mean-square scores. In this paper we address the estimation uncertainty involved in each of the points of such a FIC plot. This needs careful assessment of each of the estimators from the candidate models, taking also modelling bias into account, along with the relative precision of the associated estimated mean squared error quantities. We use confidence distributions for these tasks. This leads to fruitful CD–FIC plots, helping the statistician to judge to what extent the seemingly best models really are better than other models, etc. These efforts also lead to two further developments. The first is a new tool for model selection, which we call the quantile-FIC, which helps overcome certain difficulties associated with the usual FIC procedures, related to somewhat arbitrary schemes for handling estimated squared biases. A particular case is the median-FIC. The second development is to form model averaged estimators with weights determined by the relative sizes of the median- and quantile-FIC scores. View Full-Text
Keywords: confidence distributions; FIC plots; focused information criteria; median-FIC and quantile-FIC; model averaging; risk functions confidence distributions; FIC plots; focused information criteria; median-FIC and quantile-FIC; model averaging; risk functions
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MDPI and ACS Style

Cunen, C.; Hjort, N.L. Confidence Distributions for FIC Scores. Econometrics 2020, 8, 27. https://0-doi-org.brum.beds.ac.uk/10.3390/econometrics8030027

AMA Style

Cunen C, Hjort NL. Confidence Distributions for FIC Scores. Econometrics. 2020; 8(3):27. https://0-doi-org.brum.beds.ac.uk/10.3390/econometrics8030027

Chicago/Turabian Style

Cunen, Céline, and Nils L. Hjort 2020. "Confidence Distributions for FIC Scores" Econometrics 8, no. 3: 27. https://0-doi-org.brum.beds.ac.uk/10.3390/econometrics8030027

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