New Approaches for Censored Quantile Regression Models via Data Augmentation

在现代大数据时代，随着海量数据的可用性，异构行为是一种普遍现象。 这是一个重要的挑战，开发统计方法，从表现出异质性的数据集提取有用的见解，而不作出强有力的建模假设，可能会限制这些方法的适用性。一种有效的方法是以协变量为条件对结果变量的分位数建模，这种方法称为分位数回归。当前的项目开发新的统计方法和计算技术的分位数回归模型时，一些观察只有部分观察。拟议的研究将使使用丰富的分位数回归模型的一个大类的应用程序，以前不适合这些技术。 拟议的框架将包括高维设置，其中协变量的数量可能会超过观察的数量，这在许多生物学，医学和经济学应用中很常见。这项研究将在科学期刊、会议和研讨会上广泛传播，并将开发R语言软件包。 由于拟议的研究被放置在现代统计方法，计算和理论与大量应用的交叉点，它将适合培养具有广泛技能的研究生。该研究将为分位数回归模型在任意删失下的统计分析提供新的有效方法，即在同一数据集内可能出现单删失、双删失和区间删失等多种删失类型，且协变量可能是高维的。 在这个项目中，将考虑三个基本问题，在截尾分位数建模：（i）任意截尾下开发有效的推理方法，并研究其理论性质，（ii）设计计算可扩展的算法，具有统计上理想的性能，可以处理高维协变量，（iii）开发模型，考虑具有异质分位数效应的子群。 一个基本的挑战，将解决的是如何数据扩增和贝叶斯框架可以有效地利用时，一个明确的可能性是不可用的。该方法的一个重要特点是其计算的可扩展性，同时具有理想的统计属性。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

With the availability of massive amounts of data in the modern Big Data era, heterogeneous behavior is a common phenomenon. It is an important challenge to develop statistical methods for extracting useful insights from datasets exhibiting heterogeneity, without making strong modeling assumptions that could restrict the applicability of these methods. One efficient way of doing this is to model the quantiles of an outcome variable conditional on covariates, a method referred to as quantile regression. The current project develops novel statistical methods and computational techniques for quantile regression models when some of the observations are only partially observed. The proposed research will enable the use of the rich class of quantile regression models for a large class of applications that were previously not amenable to these techniques. The proposed framework will include the high-dimensional setting where the number of covariates could potentially exceed the number of observations, a common occurrence in many biological, medical, and economics applications. The research will be broadly disseminated in scientific journals, at conferences and seminars, and software packages in R will be developed. As the proposed research is placed at the intersection of modern statistical methodology, computation, and theory with substantial applications, it will be suitable for training graduate students with a broad range of skills. The proposed research will develop novel and efficient statistical methods for quantile regression models when the responses are subject to arbitrary censoring, that is, multiple censoring types including single, double and interval censoring can occur within the same dataset, and the covariates can be high-dimensional. Three fundamental problems in censored quantile modeling will be considered in this project: (i) develop efficient inferential methods under arbitrary censoring and study their theoretical properties, (ii) devise computationally scalable algorithms having statistically desirable properties that can handle high-dimensional covariates, and (iii) develop models that account for subgroups having heterogeneous quantile effects. A fundamental challenge that will be tackled is how data augmentation and the Bayesian framework can be efficiently utilized when an explicit likelihood is unavailable. An important feature of the methods is their computational scalability while having desirable statistical properties.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.