In the analysis of large spatial datasets, identifying and treating spatial outliers is essential for accurately interpreting geographical phenomena. While spatial correlation measures, particularly Local Indicators of Spatial Association (LISA), are widely used to detect spatial patterns, the presence of abnormal observations frequently distorts the landscape and conceals critical spatial relationships. These outliers can significantly impact analysis due to the inherent spatial dependencies present in the data. Traditional influence function (IF) methodologies, commonly used in statistical analysis to measure the impact of individual observations, are not directly applicable in the spatial context because the influence of an observation is determined not only by its own value but also by its spatial location, its connections with neighboring regions, and the values of those neighboring observations. In this paper, we introduce a local version of the influence function (LIF) that accounts for these spatial dependencies. Through the analysis of both simulated and real-world datasets, we demonstrate how the LIF provides a more nuanced and accurate detection of spatial outliers compared to traditional LISA measures and local impact assessments, improving our understanding of spatial patterns.

翻译：在大型空间数据集的分析中，识别和处理空间异常值对于准确解释地理现象至关重要。虽然空间相关性度量，特别是局部空间关联指标（LISA），被广泛用于检测空间模式，但异常观测的存在常常扭曲空间格局并掩盖关键的空间关系。由于数据中固有的空间依赖性，这些异常值可能对分析产生显著影响。传统的影响函数（IF）方法在统计分析中常用于衡量个体观测的影响，但由于观测的影响不仅由其自身值决定，还取决于其空间位置、与邻近区域的连接以及邻近观测的值，因此这些方法无法直接应用于空间背景。本文提出了一种考虑这些空间依赖性的局部影响函数（LIF）版本。通过对模拟和真实数据集的分析，我们证明了与传统LISA度量和局部影响评估相比，LIF能够提供更细致、更准确的空间异常值检测，从而增进我们对空间模式的理解。