Identifying dependency between two random variables is a fundamental problem. Clear interpretability and ability of a procedure to provide information on the form of the possible dependence is particularly important in evaluating dependencies. We introduce a new estimator of the quantile dependence function and pertinent local acceptance regions. This leads to insightful visualization and evaluation of 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. Large-sample consistency of the proposed test is also proved. We show that, in terms of power, new test is one of the best statistics for independence testing when considering a wide range of alternative models. Finally, we demonstrate use of our approach to visualize dependence structure and to detect local departures from independence through analyzing some datasets.

翻译：识别两个随机变量之间的依赖关系是一个基础性问题。在评估依赖关系时，方法的清晰可解释性以及其提供潜在依赖形式信息的能力尤为重要。我们引入了一种新的分位数依赖函数估计量及其相关的局部接受域。这为底层依赖结构提供了深刻的视觉化与评估手段。我们还提出了一种与此新估计量相关的、用于检验两个随机变量独立性的测试。我们的方法基于秩统计量，并推导出一个有限样本理论，该理论保证了我们的解决方案在任何给定样本量下的推断有效性。这些方法易于实现且计算高效。我们还证明了所提出检验的大样本一致性。研究表明，在考虑广泛的备择模型时，新检验在功效方面是独立性检验的最佳统计量之一。最后，我们通过分析若干数据集，展示了如何使用我们的方法来可视化依赖结构并检测局部偏离独立性的情况。