Most normality tests in the literature are performed for scalar and independent samples. Thus, they become unreliable when applied to colored processes, hampering their use in realistic scenarios. We focus on Mardia's multivariate kurtosis, derive closed-form expressions of its asymptotic distribution for statistically dependent samples, under the null hypothesis of normality. Included experiments illustrate, by means of copulas, that it does not suffice to test a one-dimensional marginal to conclude normality. The proposed test also exhibits good properties on other typical scenarios, such as the detection of a non-Gaussian process in the presence of an additive Gaussian noise.
翻译：文献中的大多数正常测试是针对标度和独立样品进行的,因此,在应用有色过程时,这些测试变得不可靠,妨碍了在现实情况下使用这些测试。我们侧重于马尔迪亚的多变曲线,在正常性的无效假设下,为统计上依赖的样本得出其无症状分布的封闭式表达方式。包括试样在内的实验通过阳极来说明,测试一维边缘不足以得出正常状态。提议的测试还显示了其他典型情景的良好特性,例如,在加注高山噪音的情况下检测非高山进程。
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