In this paper, we consider a spatial linear model under the multivariate Student’s t-distribution with finite second moment. This distribution, which contains the normal distribution, offers a more flexible framework for modelling spatial data. We use a reparameterized version of the multivariate Student’s t-distribution, so that the scale matrix corresponds to the covariance matrix of the spatial data. The main goal of this work is to develop influence measures to detect presence of influential observations and possible outliers, based on the likelihood displacement and on the score statistics. A heteroskedastic model is considered as a perturbation scheme to the covariance matrix of t-Student spatial linear model. Identifiability issues and robustness aspects of the maximum likelihood estimators are also discussed. The results are illustrated using a soybean yield real data and a simulation study.

在本文中，我们考虑具有有限第二矩的多元t-学生分布下的空间线性模型。这种包含正态分布的分布为建模空间数据提供了更为灵活的框架。我们使用多元t-学生分布的重新参数化版本，以便比例矩阵对应于空间数据的协方差矩阵。这项工作的主要目标是根据似然位移和得分统计数据，开发影响力检测方法，以检测有影响的观察结果和可能的异常值。异方差模型被认为是t协方差矩阵的摄动方案-学生空间线性模型。还讨论了最大似然估计器的可识别性问题和鲁棒性方面。使用大豆产量真实数据和模拟研究说明了结果。