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-party liability insurance portfolio, the proposed method effectively estimates risk measures such as the conditional Value-at-Risk and Expected Shortfall. This result suggests that this semiparametric approach can serve as an alternative in insurance risk management.

翻译：理解变量之间的依赖关系，特别是给定一组协变量后揭示其统计特性，为基于观测情景的风险分析和决策制定等实际运营管理提供了数学基础。本文提出了一种基于分布回归和分解方法对双变量结果的条件联合分布进行建模的估计方法。该方法属于半参数方法，允许在无需对整个分布施加全局参数假设的条件下，灵活地对给定协变量的边际分布和联合分布进行建模。与现有参数方法相比，该方法能处理离散、连续或混合变量，并以简单有效的方式捕捉双变量结果与协变量之间的分布依赖结构。多项模拟结果表明，在有限样本下，该方法的表现与替代方法相当或更优。在机动车第三方责任险投资组合的应用研究中，该方法有效估算了条件风险价值（Conditional Value-at-Risk）和期望损失（Expected Shortfall）等风险度量指标。这一结果表明，该半参数方法可作为保险风险管理中的一种替代方案。