Analysis of incomplete data in quantile regression and semiparametric models

首席调查员(PI)的目标是开发新的统计方法，使用分位数回归来分析不完整数据，其中不完整数据的原因是由于审查或测量误差。这项研究具有挑战性，主要是因为分位数回归的目的是避免参数误差分布假设，因此不能使用标准的基于似然的方法。PI将专注于三个不同但相关的问题。首先，将开发新的基于校正分数的估计方法，以解决协变量中的一类测量误差。其次，为了适应高维协变量，提出了一种基于指数的删失分位数回归估计方法。将为变量选择制定惩罚方法。第三个问题集中在协变量受固定审查的数据上。为了提高完全样本估计的效率，提出了一种新的基于分位数删失回归的多重补偿方法。新的补偿方法不仅可用于改善分位数回归问题的统计推断，还可用于更一般回归问题的统计推断。该研究将在各个领域具有广泛和有价值的适用性，例如，在基因表达数据经常被错误测量的微阵列研究中，在随机审查普遍存在的生存研究中，以及在测量结果经常受到固定审查的环境和地质研究中。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不同影响。该项目将通过开发高级专题课程来整合研究和教育，指导学生，特别是来自代表性不足群体的学生。

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.