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

分位数回归提供了一个有价值的半参数工具，用于对给定预测值的响应变量的条件分位数进行建模。然而，在数据稀疏的区域，例如在分位数水平接近0或1的低或高分位数区域，进行分位数回归的推理是具有挑战性的。在拟议的研究中，首席调查者(PI)旨在发展数据稀疏区域的分位数回归的理论和方法，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计划开发基于极值理论的新应用的外推方法。在数据稀疏领域，模型的建立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。将开发用于联合分位数估计和分位数间收缩的新理论和方法，以通过在多个分位数函数之间共享信息来提高统计效率。PI还将研究相依数据的尾部分位数回归，其中关于相依对统计推断的影响的普遍理解需要重新检查。在许多领域中的一个重要问题是对罕见但具有重大后果的事件的建模和预测。出人意料的强降雨、巨额投资组合损失和危险的低出生体重都是罕见事件的一些例子。对于这类事件，科学家们特别感兴趣的是对潜在分布的尾部分位数进行建模和估计，而不是像平均值或中位数这样的中央总结。拟议的方法将在气候科学中罕见事件的研究、金融风险管理、婴儿出生体重研究和保险索赔预测中具有广泛和有价值的应用。PI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，并通过培训高中教师，接触到K-12教育水平，从而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.