Regional data analysis is concerned with the analysis and modeling of measurements that are spatially separated by specifically accounting for typical features of such data. Namely, measurements in close proximity tend to be more similar than the ones further separated. This might hold also true for cross-dependencies when multivariate spatial data is considered. Often, scientists are interested in linear transformations of such data which are easy to interpret and might be used as dimension reduction. Recently, for that purpose spatial blind source separation (SBSS) was introduced which assumes that the observed data are formed by a linear mixture of uncorrelated, weakly stationary random fields. However, in practical applications, it is well-known that when the spatial domain increases in size the weak stationarity assumptions can be violated in the sense that the second order dependency is varying over the domain which leads to non-stationary analysis. In our work we extend the SBSS model to adjust for these stationarity violations, present three novel estimators and establish the identifiability and affine equivariance property of the unmixing matrix functionals defining these estimators. In an extensive simulation study, we investigate the performance of our estimators and also show their use in the analysis of a geochemical dataset which is derived from the GEMAS geochemical mapping project.

翻译：区域数据分析涉及通过具体计算这些数据的典型特征而在空间上进行空间分离的测量的分析和建模。也就是说,近距离测量往往比进一步分离的测量更加相似。如果考虑多变空间数据,这在交叉依赖性方面可能也是一样。通常,科学家对这些数据的线性转换感兴趣,这些数据易于解释,并可能用作减少尺寸。最近,为此目的,引入了空间盲源分离(SBSS),其中假定观察到的数据是由不相关、不固定的随机字段的线性混合组成的。然而,在实际应用中,当空间范围扩大时,薄弱的定点假设可能遭到违反,因为第二顺序依赖性在导致非静止分析的领域有所不同。在我们的工作中,我们扩展SBSS模型,以适应这些定点性违规情况,提出了三个新的估计,确定了界定这些定点的不固定性矩阵功能的辨别性和不均匀性属性。在进行一项广泛的模拟研究中,我们从地质化学分析中得出的地质化学分析结果。