Distances in Robust Model Selection

干净的数据是大多数统计分析的先决条件。当出现可疑数据项时，理想的解决方案是返回检查源。然而，在许多情况下，这是不可能的。因此，污染是一个重要的问题，需要能够处理大型数据集的强大技术来处理这个问题。研究了距离在鲁棒模型选择问题中的作用。本文认为，稳健模型的评估和选择是一个重要的问题，但在文献中没有得到足够的重视。有人建议，距离为解决建模问题的各个方面提供了潜在的有价值的工具，其中一个是鲁棒性方面。提出了至少在两个方面不同于经典鲁棒性范式的新框架。经典鲁棒性的发展大多围绕着位置尺度模型及其概念。将经典稳健程序扩展到其他非位置尺度模型的尝试取得了有限的成功。这里提出的方法很容易结合各种各样的模型，包括位置尺度模型。新提议的出发点是确定拟合优度度量，该度量提供了对给定模型是否接近生成数据的机制的评估。然后检查在什么意义上的措施是稳健的。距离已经广泛应用于许多科学领域，如遗传学、物理学、社会学、人类学，以及最近的机器学习领域。这项工作的意义是双重的。在统计科学领域，提供了一个非常通用的框架，它可以解决稳健模型评估和选择的问题，可以处理大型数据集，并允许测量模型接近所研究现象的程度。在统计领域之外，技术和科学成果可以扩展并应用于解决临床信息学和生物等效性中的重要问题。

Clean data is prerequisite for most statistical analyses. An ideal solution, when questionable data items arise, is to go back to check the source. However, in many cases this is not possible. Contamination therefore is an important problem, and robust techniques that can handle large data sets are needed to cope with this problem. The role of distances in the problem of robust model selection is examined. It is argued that robust model assessment and selection is an important problem that has not received adequate attention in the literature. It is suggested that distances offer potentially valuable tools for addressing various aspects of the problem of modeling, one of which is the aspect of robustness. A new framework is proposed that differs from the classical robustness paradigm in at least two aspects. Most of the developments in classical robustness center around location-scale models and the concepts therefrom. Attempts to extend classical robust procedures to other non location-scale models were met with limited success. The methodology proposed here incorporates easily a wide variety of models, including location-scale models. The starting point of the new proposal is the identification of a goodness-of-fit measure that provides an assessment of whether a given model approximates the mechanism that generated the data. It is then examined in what sense the measure is robust. Distances have been used extensively in many scientific fields such as genetics, physics, sociology, anthropology and more recently in the field of machine learning. The significance of this work is two-fold. Within the scientific field of statistics, a very general framework, that can address the problem of robust model assessment and selection is offered, that can handle large data sets and allows to measure the extend to which the model approximates the phenomenon under study. Outside the field of statistics the technology and scientific results can be extended and applied to address important problems in clinical informatics and bioequivalence.