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New Approaches for Censored Quantile Regression Models via Data Augmentation

通过数据增强的截尾分位数回归模型的新方法

基本信息

批准号：
1811768
负责人：
Naveen Naidu Narisetty
金额：
$ 15万
依托单位：
University of Illinois at Urbana-Champaign
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-05-15 至 2022-04-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1811768&HistoricalAwards=false
关键词：
New Approaches Censored Quantile Regression

项目摘要

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.

随着现代大数据时代海量数据的可获得性，异构性行为是一种普遍现象。一个重要的挑战是开发统计方法，以便从表现出异质性的数据集中提取有用的见解，而不做出可能限制这些方法适用性的强有力的建模假设。要做到这一点，一种有效的方法是根据协变量对结果变量的分位数进行建模，这种方法称为分位数回归。目前的项目为分位数回归模型开发了新的统计方法和计算技术，当一些观测只被部分观察到时。拟议的研究将使丰富的分位数回归模型能够用于以前不适用于这些技术的大类应用。建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都是常见的。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的软件包。由于拟议的研究处于现代统计方法、计算和理论的交汇点，具有实质性的应用，因此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截尾情况下的统计方法提供新的、有效的方法，即在同一数据集中可以出现包括单截尾、双截尾和区间截尾在内的多种截尾类型，并且协变量可以是高维的。本项目将考虑删失分位数建模中的三个基本问题：(I)开发任意删减下的有效推理方法，并研究其理论性质；(Ii)设计具有统计期望性质的可计算可扩展的算法，其能够处理高维协变量；以及(Iii)开发解释具有不同分位数效应的子组的模型。将解决的一个根本挑战是，当无法获得明确的可能性时，如何有效地利用数据增强和贝叶斯框架。这些方法的一个重要特征是它们的计算可扩展性，同时具有理想的统计特性。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。