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建模的条件分位数的响应变量给定的预测。然而，在数据稀疏的区域中，例如在分位数水平接近0或1的低分位数或高分位数处，对分位数回归进行推断是具有挑战性的。在拟议的研究中，主要研究者（PI）的目标是开发数据稀疏区域中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计划基于极值理论的新应用开发外推方法。在数据稀少的地区，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。将开发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还将研究依赖性数据的尾部分位数回归，其中需要重新检查关于依赖性对统计推断影响的共识。因此，新的和有效的方法，以纳入tail dependency.A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。出乎意料的强降雨，大量的投资组合损失，以及危险的低出生体重是罕见事件的一些例子。对于这类事件，科学家特别感兴趣的是建模和估计潜在分布的尾部分位数，而不是中心摘要，如平均值或中位数。所提出的方法将在气候科学中的罕见事件研究、金融风险管理、婴儿出生体重研究和保险索赔预测等方面具有广泛而有价值的应用。PI将通过开发高级主题课程，让研究生和本科生，特别是那些来自代表性不足的群体的学生参与该项目，并通过培训高中教师来达到K-12教育水平，从而整合研究和教育。

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.