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.

中文翻译：

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FIC分数的置信度分布

当使用聚焦信息标准（FIC）对候选模型进行评估并对​​其在给定估计任务中的表现进行排序时，通常会生成所谓的FIC图。该图在y轴上具有不同的点估计值，在x轴上具有根FIC得分，这些是估计的均方根得分。在本文中，我们解决了此类FIC图各点所涉及的估计不确定性。这需要仔细评估候选模型中的每个估计量，同时还要考虑建模偏差以及相关的估计均方误差量的相对精度。对于这些任务，我们使用置信度分布。这导致了CD–FIC绘图的成果，帮助统计学家判断看似最好的模型确实比其他模型更好，等等。这些努力还导致了进一步的发展。第一个是用于模型选择的新工具，我们称其为分位数FIC，它有助于克服与​​常规FIC程序相关的某些困难，这些困难与处理估计平方偏差的某种任意方案有关。特殊情况是中位数FIC。第二个发展是形成模型平均估计量，其权重由中位数和分位数FIC得分的相对大小确定。与处理估计的平方偏差的某种任意方案有关。特殊情况是中位数FIC。第二个发展是形成模型平均估计量，其权重由中位数和分位数FIC得分的相对大小确定。与处理估计的平方偏差的某种任意方案有关。特殊情况是中位数FIC。第二个发展是形成模型平均估计量，其权重由中位数和分位数FIC得分的相对大小确定。