Identifying dependency between two random variables is a fundamental problem. The clear interpretability and ability of a procedure to provide information on the form of possible dependence is particularly important when exploring dependencies. In this paper, we introduce a novel method that employs a new estimator of the quantile dependence function and pertinent local acceptance regions. This leads to an insightful visualisation and a rigorous evaluation of the underlying dependence structure. We also propose a test of independence of two random variables, pertinent to this new estimator. Our procedures are based on ranks, and we derive a finite-sample theory that guarantees the inferential validity of our solutions at any given sample size. The procedures are simple to implement and computationally efficient. The large sample consistency of the proposed test is also proved. We show that, in terms of power, the new test is one of the best statistics for independence testing when considering a wide range of alternative models. Finally, we demonstrate the use of our approach to visualise dependence structure and to detect local departures from independence through analysing some real-world datasets.

翻译：识别两个随机变量之间的依赖性是一个基本问题。在探索依赖关系时，程序具有清晰的解释能力并能提供可能依赖形式的信息尤为重要。本文提出了一种新方法，该方法采用分位数依赖函数的新估计量及相关的局部接受区域，从而实现对底层依赖结构具有洞察力的可视化及严格评估。我们还针对该新估计量提出了一个两个随机变量独立性的检验方案。我们的程序基于秩统计量，并推导了保证解在任何给定样本量下推断有效性的有限样本理论。该程序易于实现且计算高效。同时证明了所提检验的大样本一致性。研究表明，在考虑广泛替代模型时，新检验方法在检验效能方面堪称独立性检验的最佳统计量之一。最后，通过分析真实数据集，展示了该方法在可视化依赖结构及检测局部独立性偏离方面的应用。