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导向统计框架，用于评估成对设定中假定的高斯依赖结构。这同时涉及多元正态性和正态连接函数的拟合优度检验。该检验方法根据20/60/20法则对数据进行聚类，并在所得子集上比较条件协方差（或相关性）估计值。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，以及在多元正态性假设下的渐近枢轴分布。通过广泛的功效模拟研究，我们验证了所提框架的有效性，并表明该方法优于流行的基准备选方案。此外，我们将所提方法应用于大宗商品市场数据。