Distances in Robust Model Selection

干净的数据是大多数统计分析的先决条件。当出现有问题的数据项时，理想的解决方案是回去检查来源。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健壮技术来处理这个问题。研究了距离在稳健模型选择问题中的作用。稳健性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。有人认为，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，其中之一是稳健性方面。提出了一种新的框架，该框架至少在两个方面不同于经典的健壮性范例。经典稳健性的发展大多围绕位置-尺度模型及其概念展开。将经典的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模型，包括位置尺度模型。新提案的起点是确定拟合优度衡量标准，以评估某一特定模型是否接近产生数据的机制。然后，它被检查在什么意义上的衡量是稳健的。距离在遗传学、物理学、社会学、人类学等许多科学领域得到了广泛的应用，最近在机器学习领域也得到了广泛应用。这项工作的意义是双重的。在统计科学领域内，提供了一个非常通用的框架，可以解决稳健的模型评估和选择问题，该框架可以处理大数据集，并允许衡量模型在多大程度上接近所研究的现象。在统计学领域之外，这项技术和科学成果可以被推广和应用，以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.