Analysis of incomplete data in quantile regression and semiparametric models

分位数回归和半参数模型中不完整数据的分析

• 批准号: 1007420
• 负责人: Huixia Wang
• 金额: $ 14万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1007420&HistoricalAwards=false
• 关键词: Analysis; incomplete; data; quantile; regression

The principal investigator (PI) aims to develop new statistical methodology for analyzing incomplete data using regression of quantiles where causes of incomplete data are due to either censoring or measurement error. The research is challenging mainly because quantile regression aims to avoid parametric error distributional assumptions so the standard likelihood-based methods cannot be used. The PI will focus on three different but related problems. First, new approaches to estimation based on corrected scores will be developed to account for a class of measurement errors in the covariates. Second, an index-based estimation method will be proposed for censored quantile regression to accommodate high dimensional covariates. Penalization methods will be developed for variable selection. The third problem focuses on data with covariates subject to fixed censoring. To improve the efficiency over estimators from complete samples, a new multiple imputation approach based on censored regression of quantiles will be developed. The new imputation method can be used to improve statistical inference for not only quantile regression but also more general regression problems.The proposed research will have broad and valuable applicability in various fields, for instance, in microarray studies where the gene expression data are often measured with errors, in survival studies where random censoring is common, and in environmental and geological studies where measurements are often subject to fixed censoring. For example, in contrast to conventional statistical methods, quantile regression models can help discover heterogeneous effects of drug treatments on survival times of both high and low risk patients. The project will integrate research and education by developing advanced topics courses, mentoring students especially those from under-represented groups.

主要研究者（PI）旨在开发新的统计方法，用于使用分位数回归分析不完整数据，其中不完整数据的原因是删失或测量误差。该研究具有挑战性，主要是因为分位数回归旨在避免参数误差分布假设，因此无法使用标准的基于似然的方法。PI将关注三个不同但相关的问题。首先，将开发基于校正分数的新估计方法，以解释协变量中的一类测量误差。其次，提出一种指数基估计方法，用于删失分位数回归以适应高维协变量。将为变量选择制定惩罚方法。第三个问题集中于协变量服从固定删失的数据。为了提高完全样本估计的效率，将发展一种新的基于分位数删失回归的多重插补方法。新的插补方法不仅可以用于分位数回归的统计推断，而且可以用于更一般的回归问题，该研究将在各个领域具有广泛和有价值的应用，例如，在基因表达数据经常测量错误的微阵列研究中，在随机删失常见的生存研究中，以及在环境和地质研究中，测量经常受到固定的审查。例如，与传统的统计方法相比，分位数回归模型可以帮助发现药物治疗对高风险和低风险患者生存时间的异质性影响。该项目将通过开发高级主题课程，指导学生，特别是来自代表性不足群体的学生，将研究和教育结合起来。