Title: Rank-based concordance for zero-inflated data: New representations, estimators, and sharp bounds Show Chinese title

Title: 基于等级的一致性对于零膨胀数据：新的表示、估计量和精确界限

Abstract: Quantifying concordance between two random variables is crucial in applications. Traditional estimation techniques for commonly used concordance measures, such as Gini's gamma or Spearman's rho, often fail when data contain ties. This is particularly problematic for zero-inflated data, characterized by a combination of discrete mass in zero and a continuous component, which frequently appear in insurance, weather forecasting, and biomedical applications. This study provides a new formulation of Gini's gamma and Spearman's footrule, two rank-based concordance measures that incorporate absolute rank differences, tailored to zero-inflated continuous distributions. Along the way, we correct an expression of Spearman's rho for zero-inflated data previously presented in the literature. The best-possible upper and lower bounds for these measures in zero-inflated continuous settings are established, making the estimators useful and interpretable in practice. We pair our theoretical results with simulations and two real-life applications in insurance and weather forecasting, respectively. Our results illustrate the impact of zero inflation on dependence estimation, emphasizing the benefits of appropriately adjusted zero-inflated measures. Show Chinese abstract

Abstract: 量化两个随机变量之间的协调性在应用中至关重要。 传统的常用协调度量估计技术，如吉尼的伽马或斯皮尔曼的 rho，当数据包含结时往往失效。 这对于零膨胀数据尤其成问题，零膨胀数据的特点是零点的离散质量与连续成分相结合，在保险、天气预报和生物医学应用中经常出现。 本研究提供了一种新的吉尼的伽马和斯皮尔曼的脚则的表述，这两种基于排名的协调度量结合了绝对排名差异，适用于零膨胀连续分布。 在此过程中，我们纠正了文献中先前提出的零膨胀数据的斯皮尔曼 rho 的表达式。 建立了这些度量在零膨胀连续设置中的最佳可能上下界，使估计量在实践中具有实用性和可解释性。 我们将理论结果与模拟以及保险和天气预报中的两个实际应用相结合。 我们的结果说明了零膨胀对依赖估计的影响，强调了适当调整的零膨胀度量的好处。