As a rule statistical measures are often vulnerable to the presence of outliers and spatial correlation coefficients, critical in the assessment of spatial data, remain susceptible to this inherent flaw. In contexts where data originates from a variety of domains (such as, e. g., socio-economic, environmental or epidemiological disciplines) it is quite common to encounter not just anomalous data points, but also non-normal distributions. These irregularities can significantly distort the broader analytical landscape often masking significant spatial attributes. This paper embarks on a mission to enhance the resilience of traditional spatial correlation metrics, specifically the Moran Coefficient (MC), Geary's Contiguity ratio (GC), and the Approximate Profile Likelihood Estimator (APLE) and to propose a series of alternative measures. Drawing inspiration from established analytical paradigms, our research harnesses the power of influence function studies to examine the robustness of the proposed novel measures in the presence of different outlier scenarios.

翻译：通常而言，统计度量极易受到异常值的影响，而空间相关性系数（在空间数据评估中至关重要）同样难以摆脱这一固有缺陷。在数据源于社会经济、环境或流行病学等多学科领域的情境下，不仅异常数据点屡见不鲜，非正态分布亦属常态。这些不规则性可能显著扭曲更广泛的分析图景，往往掩盖重要的空间属性。本文旨在增强传统空间相关性度量（具体而言，即莫兰系数（MC）、杰瑞相邻比率（GC）及近似剖面似然估计量（APLE））的稳健性，并提出一系列替代指标。借鉴既有分析范式，本研究利用影响函数研究的强大能力，检验所提出的新型度量在不同异常值场景下的稳健性。