Independence and Conditional Independence (CI) are two fundamental concepts in probability and statistics, which can be applied to solve many central problems of statistical inference. There are many existing independence and CI measures defined from diverse principles and concepts. In this paper, the 16 independence measures and 16 CI measures were reviewed and then evaluated with simulated and real data. For the independence measures, eight simulated data were generating from normal distribution, normal and Archimedean copula functions to compare the measures in bivariate or multivariate, linear or nonlinear settings. Two UCI dataset, including the heart disease data and the wine quality data, were used to test the power of the independence measures in real conditions. For the CI measures, two simulated data with normal distribution and Gumbel copula, and one real data (the Beijing air data) were utilized to test the CI measures in prespecified linear or nonlinear setting and real scenario. From the experimental results, we found that most of the measures work well on the simulated data by presenting the right monotonicity of the simulations. However, the independence and CI measures were differentiated on much complex real data respectively and only a few can be considered as working well with reference to domain knowledge. We also found that the measures tend to be separated into groups based on the similarity of the behaviors of them in each setting and in general. According to the experiments, we recommend CE as a good choice for both independence and CI measure. This is also due to its rigorous distribution-free definition and consistent nonparametric estimator.
翻译:独立和有条件独立(CI)是概率和统计的两个基本概念,可用于解决统计推论的许多中心问题。现有许多独立和光学指标根据不同的原则和概念界定了多种独立和光学指标。在本文件中,对16项独立措施和16项独立措施进行了审查,然后用模拟和真实数据对之进行了评估。对于独立措施,有8项模拟数据来自正常分布、正常和Archimedean 相框函数,以比较双轨或多变量、线性或非线性环境的计量。两个UCI数据集,包括心脏病数据和葡萄酒质量数据,用来在实际条件下测试独立措施的威力。对于光学计量,有两项模拟独立和光学计量的模拟数据和光学测量,对正常分布和光学计量的模拟能力进行了测试,对正常分布和光学的模拟数据进行了区分,同时,我们从每一类的直线性或非线性设定和直线性设定和真实性环境假设中,我们发现大多数的计量和CI计量标准都是在非常复杂的领域进行。