We present a novel data-oriented statistical framework that assesses the presumed Gaussian dependence structure in a pairwise setting. This refers to both multivariate normality and normal copula goodness-of-fit testing. The proposed test clusters the data according to the 20/60/20 rule and confronts conditional covariance (or correlation) estimates on the obtained subsets. The corresponding test statistic has a natural practical interpretation, desirable statistical properties, and asymptotic pivotal distribution under the multivariate normality assumption. We illustrate the usefulness of the introduced framework using extensive power simulation studies and show that our approach outperforms popular benchmark alternatives. Also, we apply the proposed methodology to commodities market data.

翻译：我们提出一种新颖的数据驱动统计框架，用于评估成对设定下假设的高斯依赖结构。这同时涉及多元正态性和正态Copula拟合优度检验。该检验方法根据20/60/20法则对数据进行聚类，并在所得子集上对比条件协方差（或相关）估计量。相应的检验统计量具有自然的实际解释意义、理想的统计性质，且在多元正态假设下具有渐近枢纽分布。我们通过广泛的功效模拟研究展示了所提框架的实用性，并表明该方法优于流行的基准替代方案。此外，我们将该方法论应用于商品市场数据。