Most multivariate outlier detection procedures ignore the spatial dependency of observations, which is present in many real data sets from various application areas. This paper introduces a new outlier detection method that accounts for a (continuously) varying covariance structure, depending on the spatial neighborhood of the observations. The underlying estimator thus constitutes a compromise between a unified global covariance estimation, and local covariances estimated for individual neighborhoods. Theoretical properties of the estimator are presented, in particular related to robustness properties, and an efficient algorithm for its computation is introduced. The performance of the method is evaluated and compared based on simulated data and for a data set recorded from Austrian weather stations.

翻译：大多数多变量离群点检测程序忽略了观测值之间的空间依赖性，而这一特性普遍存在于多个应用领域的实际数据集中。本文提出了一种新颖的离群点检测方法，该方法考虑了随观测值空间邻域而变化的（连续）协方差结构。因此，该底层估计器在全局统一协方差估计与针对各邻域估计的局部协方差之间实现了折衷。我们给出了该估计量的理论性质，特别是与稳健性相关的性质，并引入了一种高效的算法用于计算。通过模拟数据以及奥地利气象站记录的数据集，评估并比较了该方法的性能。