A confidence distribution is a distribution for a parameter of interest based on a parametric statistical model. As such, it serves the same purpose for frequentist statisticians as a posterior distribution for Bayesians, since it allows to reach point estimates, to assess their precision, to set up tests along with measures of evidence, to derive confidence intervals, comparing the parameter of interest with other parameters from other studies, etc. A general recipe for deriving confidence distributions is based on classical pivotal quantities and their exact or approximate distributions. However, in the presence of model misspecifications or outlying values in the observed data, classical pivotal quantities, and thus confidence distributions, may be inaccurate. The aim of this paper is to discuss the derivation and application of robust confidence distributions. In particular, we discuss a general approach based on the Tsallis scoring rule in order to compute a robust confidence distribution. Examples and simulation results are discussed for some problems often encountered in practice, such as the two-sample heteroschedastic comparison, the receiver operating characteristic curves and regression models.
翻译:信任分配是一种基于参数统计模型的利害关系参数分布。因此,常年统计师与贝耶斯的后期分布的目的相同,因为它能够达到点估计,评估其准确性,与证据计量一道进行测试,得出信任间隔,将感兴趣的参数与其他研究的参数进行比较,等等。 信任分配的一般食谱以古典关键数量及其准确或近似分布为基础。然而,在观察到的数据中存在模型的误差或偏差值的情况下,古典关键数量,因而信任分布可能是不准确的。本文的目的是讨论稳健信任分配的衍生和应用。特别是,我们讨论基于Tsallis评分规则的一般方法,以便计算稳健的信任分配情况。对于实践中经常遇到的一些问题,例如两个模范的血压对比、接收器运行特征曲线和回归模型,则讨论实例和模拟结果。