Inferential Methods for Quantile Regression

虽然最小二乘回归的目标是回归模型中的条件均值函数，但分位数回归提供了关于响应变量的条件分布的更完整的信息。当种群中存在异方差或总体异质性时，它尤其有价值。为了促进分位数回归模型在更广泛的应用领域中的应用，本建议旨在开发分位数回归模型的推理程序，以解释观测中随机效应或随机截尾的存在。虽然随机效应和截尾效应已经在配备了参数似然(通常是高斯似然)的线性模型下得到了很好的研究，但当对条件分布进行标准的最小假设时，传统的推断过程并不能直接扩展到分位数回归模型。主要研究人员致力于开发新的想法和工具，以便在具有随机效应或截尾效应的分位数回归模型中进行适当的推断。拟议的研究将建立在分位数回归模型的最新发展的基础上，并纳入一些创新的想法，以开发适当的推理方法，这些方法在数学上是合理的，主要是通过大样本理论，并且在现实样本量下具有统计学意义。目前在分位数回归模型中用于统计推断的方法还不能很好地处理随机效应或随机删失。例如，基因组学中对基因芯片数据的分析会导致夸大的错误发现率，而不会将阵列效应视为随机的。拟议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置信度。PI将寻求与其他科学家的合作，以确保正在开发的方法对生物科学、健康科学、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未来的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.