Data with spatial dependence are often modeled by geoestatistical tools. In spatial regression, the mean response is described using explanatory variables with georeferenced data. This modeling frequently considers Gaussianity assuming the response follows a symmetric distribution. However, when this assumption is not satisfied, it is useful to suppose distributions with the same asymmetric behavior of the data. This is the case of the Birnbaum–Saunders (BS) distribution, which has been considered in different areas and particularly in environmental sciences due to its theoretical arguments. We propose a geostatistical model based on a new approach to quantile regression considering the BS distribution. Global and local diagnostic analytics are derived for this model. The estimation of model parameters and its local influence are conducted by the maximum likelihood method. Global influence is based on the Cook distance and it is compared to local influence, in both cases to detect influential observations, whose detection and removal can modify the conclusions of a study. We illustrate the proposed methodology applying it to environmental data, which shows this situation changing the conclusions after removing potentially influential observations. A comparison with Gaussian spatial regression is conducted.

具有空间依赖性的数据通常由地统计工具建模。在空间回归中，使用解释变量和地理参考数据来描述平均响应。假设响应遵循对称分布，则此建模经常考虑高斯性。但是，当不满足此假设时，假设分布具有相同的数据非对称行为是有用的。Birnbaum-Saunders（BS）分布就是这种情况，由于其理论论据，它已在不同领域，尤其是环境科学中得到了考虑。考虑到BS分布，我们提出了一种基于新的分位数回归方法的地统计模型。此模型派生了全局和局部诊断分析。模型参数的估计及其局部影响是通过最大似然法进行的。全局影响力基于库克距离，并且在两种情况下都将其与局部影响力进行比较，以检测有影响力的观察结果，其发现和删除会影响研究结论。我们说明了将其应用于环境数据的拟议方法，该方法显示了这种情况在删除了可能有影响的观察结果后改变了结论。与高斯空间回归进行了比较。这表明在删除可能有影响的观察结果后，这种情况改变了结论。与高斯空间回归进行了比较。这表明在删除可能有影响的观察结果后，这种情况改变了结论。与高斯空间回归进行了比较。