Inferential Methods for Quantile Regression

分位数回归的推理方法

• 批准号: 0604229
• 负责人: Xuming He
• 金额: $ 37.45万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-08-01 至 2010-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0604229&HistoricalAwards=false
• 关键词: Inferential; Methods; Quantile; Regression

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.

尽管最小二乘回归目标是回归模型中条件均值函数，但分位数回归提供了有关响应变量条件分布的更多完整信息。当人口中有异质性或一般异质性时，它特别有价值。为了促进在更广泛的应用领域中的分位数回归建模，该建议旨在为分位数回归模型制定推论程序，以说明观察值中随机效应或随机审查的存在。尽管在配备有参数和高斯的线性模型下对随机效应和审查进行了充分的研究，但是当对条件分布进行标准最小的假设时，传统的推理程序对分位数回归模型的扩展并不直接扩展。该原则研究者旨在集中尝试开发新的想法和工具，以使具有随机效应或审查的分位数回归模型的适当推断。拟议的研究将基于分位数回归建模的最新发展，并结合了一些创新的思想，以开发适当的推论方法，这些推论方法在数学上是合理的，主要是通过大型样本理论，并且在现实样本大小上具有统计学意义。目前在分位数回归模型中用于统计推断的方法未能很好地处理随机效应或随机审查。例如，对基因组学中的转基因数据的分析将导致虚假发现率膨胀，而无需将阵列效应作为随机效应。拟议的研究将开发新方法，以在基于分位数回归的应用程序范围内保持统计信心。 PI将与其他科学家进行合作，以确保所开发的方法对生物科学，健康科学，工程，经济学和金融的研究人员很有价值。拟议的活动还将涉及对未来统计研究人员的研究生培训，并为选定的本科生提供研究经验。