Inferential Methods for Quantile Regression

最小二乘回归的目标是回归模型中的条件平均函数，而分位数回归提供了关于响应变量条件分布的更完整的信息。当种群中存在异方差或普遍异质性时，它尤其有价值。为了促进分位数回归建模在更广泛的应用领域，本提案旨在开发分位数回归模型的推理程序，以解释观察中随机效应或随机审查的存在。尽管随机效应和审查已经在具有参数似然的线性模型下得到了很好的研究，通常是高斯似然，但是当对条件分布做出标准最小假设时，传统的推理程序不能直接扩展到分位数回归模型。主要研究者的目的是在发展新的思路和工具，使可能适当的推理与随机效应或审查分位数回归模型集中尝试。拟议的研究将建立在分位数回归模型的最新发展基础上，并结合一些创新思想，以发展适当的推理方法，这些方法主要通过大样本理论在数学上证明是合理的，并且在实际样本量上具有统计意义。目前可用的分位数回归模型的统计推断方法尚不能很好地处理随机效应或随机审查。例如，基因组学中对GeneChip数据的分析，如果不考虑阵列效应是随机的，就会导致错误发现率的膨胀。提出的研究将开发新的方法，在更广泛的基于分位数回归的应用中保持统计信心。PI将寻求与其他科学家合作，以确保正在开发的方法对生物科学、卫生科学、工程学、经济学和金融学的研究人员有价值。拟议的活动还将包括为将来的统计研究人员培训研究生，以及为选定的本科生提供研究经验。

While least squares regression targets the conditional mean function in a regression model, quantile regression provides more complete information on the conditional distribution of the response variable. It is especially valuable when there is heteroscedasticity or general heterogeneity in the population. To facilitate quantile regression modelling in a wider areas of applications, this proposal aims to develop inferential procedures for quantile regression models to account for the presence of random-effects or random censoring in the observations. Although random-effects and censoring have been well studied under linear models equipped with parametric, and often Gaussian, likelihoods, the conventional inference procedures do not have straightforward extensions to the quantile regression model when standard minimal assumptions are made on the conditional distributions. The principle investigator aims to make focused attempts in developing new ideas and tools to make possible appropriate inference in quantile regression models with random-effects or with censoring. The proposed research will build upon the recent developments in quantile regression modelling and incorporate some innovative ideas to develop appropriate inferential methods that are mathematically justified, mainly through large sample theory, and statistically meaningful at realistic sample sizes. Currently available methods for statistical inference in quantile regression models are not well-developed to handle random-effects or random censoring. For example, the analysis of GeneChip data in genomics would result in inflated false discovery rates without taking the array effect as random. The proposed research will develop new methods that preserve statistical confidence in a wider range of quantile regression based applications. The PI will pursue collaboration with other scientists to ensure that the methodologies under development are valuable to researchers in the biological sciences, health sciences, engineering, economics, and finance. The proposed activities will also involve training of graduate students for future researchers in statistics as well as providing selected undergraduate students with research experience.