CAREER: A new and pragmatic framework for modeling and predicting conditional quantiles in data-sparse regions

分位数回归为给定预测因子的响应变量的条件分位数建模提供了有价值的半参数工具。然而，在数据稀疏的区域（例如在分位数水平接近0或1的低分位数或高分位数）中，对分位数回归进行推断是具有挑战性的。在本研究中，主要研究者（PI）旨在发展数据稀疏区域的分位数回归理论和方法，这为分位数回归开辟了一个重要的新方向。为了估计响应分布的极端条件分位数，PI计划基于极值理论的新应用开发外推方法。在数据稀疏区域，模型的制定起着至关重要的作用。PI将研究具有不同复杂程度的模型，这需要不同的技术来量化尾部分位数。将发展联合分位数估计和分位数间收缩的新理论和方法，通过在多个分位数函数之间共享信息来提高统计效率。PI还将研究依赖数据的尾分位数回归，其中需要重新检查关于依赖对统计推断影响的共同理解。因此，将提出新的有效的方法来考虑尾部依赖性。在许多领域的一个重要问题是建模和预测的事件是罕见的，但有重大后果。意外的强降雨、大量的投资损失和危险的低出生体重是一些罕见事件的例子。对于这样的事件，科学家们特别感兴趣的是建模和估计潜在分布的尾部分位数，而不是像平均值或中位数这样的中心摘要。所提出的方法将在气候科学的罕见事件研究、金融风险管理、婴儿出生体重研究和保险索赔预测方面具有广泛而有价值的应用。该项目将通过开发高级专题课程、吸引研究生和本科生（特别是来自代表性不足群体的学生）参与该项目，以及通过培训高中教师，将研究与教育结合起来。

Quantile regression provides a valuable semiparametric tool for modeling the conditional quantiles of a response variable given predictors. However, making inference for quantile regression is challenging in data-sparse regions such as at low or high quantiles with quantile levels close to 0 or 1. In the proposed research, the Principal Investigator (PI) aims to develop theory and methodology for quantile regression in data-sparse regions, which opens up a significant new direction in quantile regression. For estimating extreme conditional quantiles of the response distribution, the PI plans to develop extrapolation methods based on a novel application of the extreme value theory. In data sparse areas, the formulation of models plays a critical role. The PI will study models with different levels of complexity, which calls for different techniques for quantifying the tail quantiles. New theory and methods for joint quantile estimation and inter-quantile shrinkage will be developed to improve statistical efficiency by sharing information across multiple quantile functions. The PI will also study tail quantile regression for dependent data, where the common understanding about the impact of dependence on statistical inference needs to be re-examined. As a result, new and efficient methods to incorporate tail dependence will be proposed.An important problem in many fields is the modeling and prediction of events that are rare but have significant consequences. Unexpectedly heavy rainfall, large portfolio loss, and dangerously low birth weight are some examples of rare events. For such events, scientists are particularly interested in modeling and estimating the tail quantiles of the underlying distribution rather than the central summaries such as the mean or median. The proposed methodologies will have broad and valuable applications in studies of rare events in climate sciences, risk management in finance, studies of infant birth weights, and prediction of insurance claims. The PI will integrate research and education by developing advanced topics courses, engaging graduate and undergraduate students, especially those from under-represented groups, in the project, and reaching out to the K-12 education levels by training high school teachers.