Analysis of incomplete data in quantile regression and semiparametric models

主要研究者（PI）的目的是开发新的统计方法来分析不完整的数据使用分位数的回归，其中不完整的数据的原因是由于审查或测量误差。研究的挑战性主要在于分位数回归旨在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将关注三个不同但相关的问题。首先，将开发基于修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，将提出一种基于索引的估计方法，用于屏蔽分位数回归以适应高维协变量。将针对变量选择制定惩罚方法。第三个问题侧重于具有固定审查的协变量的数据。为了提高全样本估计器的效率，本文提出了一种基于截尾分位数回归的多重插值方法。该方法不仅可以改善分位数回归的统计推断，还可以改善一般回归问题的统计推断。拟议的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测量有误差的微阵列研究中，在随机审查常见的生存研究中，以及在测量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。

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.