Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision making given observed circumstances. This article presents an estimation method for modeling the conditional joint distribution of bivariate outcomes based on the distribution regression and factorization methods. This method is considered semiparametric in that it allows for flexible modeling of both the marginal and joint distributions conditional on covariates without imposing global parametric assumptions across the entire distribution. In contrast to existing parametric approaches, our method can accommodate discrete, continuous, or mixed variables, and provides a simple yet effective way to capture distributional dependence structures between bivariate outcomes and covariates. Various simulation results confirm that our method can perform similarly or better in finite samples compared to the alternative methods. In an application to the study of a motor third-part liability insurance portfolio, the proposed method effectively estimates risk measures such as the conditional Value-at-Risks and Expexted Sortfall. This result suggests that this semiparametric approach can serve as an alternative in insurance risk management.

翻译：理解变量间的依赖性，特别是在给定一组协变量条件下揭示其统计特性，为风险分析及在观测情景下的决策等实际运营管理提供了数学基础。本文提出一种基于分布回归与分解方法的双变量条件联合分布建模估计方法。该方法被视为半参数方法，其允许在不对整个分布施加全局参数假设的前提下，灵活建模条件于协变量的边际分布与联合分布。与现有参数方法相比，我们的方法可处理离散、连续或混合变量，并以简洁有效的方式捕获双变量结果与协变量之间的分布依赖结构。多种模拟结果表明，在有限样本下该方法的表现可与替代方法相当或更优。在应用于第三方汽车责任保险组合研究时，所提方法有效估计了条件风险价值与预期损失等风险度量。该结果表明，这一半参数方法可作为保险风险管理中的一种替代方案。