In this article, we present the bivariate and multivariate functional Moran's I statistics and multivariate functional areal spatial principal component analysis (mfasPCA). These methods are the first of their kind in the field of multivariate areal spatial functional data analysis. The multivariate functional Moran's I statistic is employed to assess spatial autocorrelation, while mfasPCA is utilized for dimension reduction in both univariate and multivariate functional areal data. Through simulation studies and real-world examples, we demonstrate that the multivariate functional Moran's I statistic and mfasPCA are powerful tools for evaluating spatial autocorrelation in univariate and multivariate functional areal data analysis.

翻译：本文提出了双变量与多元功能莫兰I统计量以及多元功能区域空间主成分分析（mfasPCA）。这些方法是多元区域空间功能数据分析领域的首创。多元功能莫兰I统计量用于评估空间自相关性，而mfasPCA则用于单变量与多元功能区域数据的降维处理。通过模拟研究和实际案例，我们证明多元功能莫兰I统计量与mfasPCA是评估单变量及多元功能区域数据分析中空间自相关性的有力工具。