Multivariate functional data are frequently obtained in many scientific or industrial areas where several functions for a statistical unit are observed over time. It is often interesting to check if the mean vector functions of two multivariate functional samples are equal. To address this important issue, two global tests for the above two-sample problem for multivariate functional data are proposed and studied. Their asymptotic random expressions under the null and certain local alternative hypotheses are derived and their root-$n$ consistencies are established. Simulation studies show that the proposed two tests generally have higher or not worse powers than some existing competitors. A real data application illustrates the proposed tests.

多变量功能数据通常在许多科学或工业领域中获得，在这些领域中，随着时间的推移会观察到一个统计单位的多个功能。检查两个多元函数样本的平均向量函数是否相等通常很有趣。为了解决这个重要问题，针对上述多元函数数据的两个样本问题，提出并研究了两个全局检验。推导了他们在零假设和某些局部替代假设下的渐近随机表达式，并且它们的根是$ñ$建立一致性。仿真研究表明，所提出的两项测试通常具有比某些现有竞争对手更高或更低的功效。实际数据应用程序说明了建议的测试。