Extensive literature exists on how to test for normality, especially for identically and independently distributed (i.i.d) processes. The case of dependent samples has also been addressed, but only for scalar random processes. For this reason, we have proposed a joint normality test for multivariate time-series, extending Mardia's Kurtosis test. In the continuity of this work, we provide here an original performance study of the latter test applied to two-dimensional projections. By leveraging copula, we conduct a comparative study between the bivariate tests and their scalar counterparts. This simulation study reveals that one-dimensional random projections lead to notably less powerful tests than two-dimensional ones.

翻译：关于如何进行正常性测试,特别是相同和独立分布的(一.d)过程的正常性测试,有广泛的文献存在。依赖样本的案例也得到了处理,但只是用于标量随机过程。因此,我们提议对多变时间序列进行联合正常性测试,扩大Mardia的科松松病测试。在这项工作的连续性方面,我们在此提供对后一种测试的初始性能研究,该测试应用于二维预测。我们通过利用千叶,对双变体测试及其标量对等进行一项比较研究。这一模拟研究表明,单维随机预测导致的测试明显不如二维测试那么有力。