Muehlmann C, De Iaco S, Nordhausen K
Institute of Statistics and Mathematical Methods in Economics, TU Wien / Technische Universität Wien / Vienna University of Technology, Vienna, Austria.
Department of Economic Sciences-Sect. of Mathematics and Statistics, University of Salento, Lecce, Italy.
Stoch Environ Res Risk Assess. 2023;37(4):1593-1613. doi: 10.1007/s00477-022-02348-2. Epub 2022 Dec 30.
With advances in modern worlds technology, huge datasets that show dependencies in space as well as in time occur frequently in practice. As an example, several monitoring stations at different geographical locations track hourly concentration measurements of a number of air pollutants for several years. Such a dataset contains thousands of multivariate observations, thus, proper statistical analysis needs to account for dependencies in space and time between and among the different monitored variables. To simplify the consequent multivariate spatio-temporal statistical analysis it might be of interest to detect linear transformations of the original observations that result in straightforward interpretative, spatio-temporally uncorrelated processes that are also highly likely to have a real physical meaning. Blind source separation (BSS) represents a statistical methodology which has the aim to recover so-called latent processes, that exactly meet the former requirements. BSS was already successfully used in sole temporal and sole spatial applications with great success, but, it was not yet introduced for the spatio-temporal case. In this contribution, a reasonable and innovative generalization of BSS for multivariate space-time random fields (stBSS), under second-order stationarity, is proposed, together with two space-time extensions of the well-known algorithms for multiple unknown signals extraction (stAMUSE) and the second-order blind identification (stSOBI) which solve the formulated problem. Furthermore, symmetry and separability properties of the model are elaborated and connections to the space-time linear model of coregionalization and to the classical principal component analysis are drawn. Finally, the usefulness of the new methods is shown in a thorough simulation study and on a real environmental application.
随着现代世界技术的进步，在实践中经常会出现显示空间和时间依赖性的大型数据集。例如，不同地理位置的多个监测站会对多种空气污染物的每小时浓度测量值进行数年的跟踪。这样的数据集包含数千个多变量观测值，因此，适当的统计分析需要考虑不同监测变量之间的空间和时间依赖性。为了简化随之而来的多变量时空统计分析，检测原始观测值的线性变换可能会很有意义，这些变换会产生直接可解释的、时空不相关的过程，并且很可能具有实际物理意义。盲源分离（BSS）是一种统计方法，旨在恢复所谓的潜在过程，这些过程恰好满足上述要求。BSS已经在单一时间和单一空间应用中成功使用，但尚未引入到时空情况中。在本文中，提出了一种在二阶平稳性下对多变量时空随机场（stBSS）进行合理且创新的BSS推广方法，以及用于提取多个未知信号的著名算法（stAMUSE）和二阶盲识别（stSOBI）的两种时空扩展方法，它们解决了所提出的问题。此外，阐述了模型的对称性和可分离性属性，并建立了与时空协区域化线性模型和经典主成分分析的联系。最后，通过全面的模拟研究和实际环境应用展示了新方法的实用性。
