权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Inference for High Dimensional Quantile Regression

高维分位数回归的推理

基本信息

批准号：
1712760
负责人：
Feifang Hu
金额：
$ 12.5万
依托单位：
George Washington University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-09-01 至 2022-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1712760&HistoricalAwards=false
关键词：
Inference Dimensional Quantile Regression

项目摘要

Quantile regression is emerging as an important and active research area driven by diverse applications. Compared with the conventional least squares regression, quantile regression methods are robust against outliers and can capture heterogeneity. In recent years, significant results related to estimation and variable selection for quantile regression have been obtained for big data applications. However, there exists little work on inferential methods including hypothesis testing and confidence interval construction for quantile regression in the high-dimensional setting. This project seeks to develop new statistical theory, methodology and algorithms to address inference problems in high-dimensional quantile regression. The research is motivated by a large clinical trial of diabetes intervention, and the developed methods can also be applied to data from genome-wide association studies, neuroscience, and environmental studies. The research will focus on two main directions. First, new testing procedures will be developed to assess the overall significance of high-dimensional covariates on quantiles of the response distribution. Two types of tests are proposed, including a maximum-type statistic based on marginal quantile regression, and a score-type statistic. Theory and methods for both fixed and diverging dimensions will be studied. Second, focusing on high-dimensional quantile regression without the conventional minimum signal strength condition on the coefficients, the PI will rigorously study the asymptotic theory of penalized estimators and develop valid post-selection inference methods based on both asymptotic theory and bootstrap procedures. 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 K-12 students and developing countries through collaboration and knowledge sharing.

分位数回归是一个重要的和活跃的研究领域，由不同的应用驱动。与传统的最小二乘回归方法相比，分位数回归方法对异常值具有鲁棒性，并且可以捕获异质性。近年来，在大数据应用中，分位数回归的估计和变量选择方面取得了重要成果。然而，在高维环境下，关于分位数回归的假设检验和置信区间构造等推理方法的研究却很少。本计画旨在发展新的统计理论、方法与演算法，以解决高维分位数回归中的推论问题。这项研究的动机是糖尿病干预的大型临床试验，所开发的方法也可以应用于全基因组关联研究，神经科学和环境研究的数据。研究将集中在两个主要方向。首先，将开发新的检验程序，以评估响应分布分位数上高维协变量的总体显著性。提出了两种类型的测试，包括基于边际分位数回归的最大型统计量和得分型统计量。将研究固定和发散维度的理论和方法。第二，专注于高维分位数回归，没有传统的最小信号强度条件的系数，PI将严格研究惩罚估计量的渐近理论，并开发有效的后选择推理方法的基础上渐近理论和自助程序。 PI将通过开发高级主题课程，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，并通过合作和知识共享接触K-12学生和发展中国家，将研究和教育结合起来。