Efficient Modeling in Quantile Regression

分位数回归的高效建模

• 批准号: 1007396
• 负责人: Xuming He
• 金额: --
• 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: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2012-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1007396&HistoricalAwards=false
• 关键词: Efficient; Modeling; Quantile; Regression

Quantile regression has in recent years emerged successfully as a powerful supplement to the more conventional least squares regression. By modeling the conditional quantile functions, the researchers are often able to gain a much more comprehensive picture of how a response variable is associated with its covariates. The prevailing approach in quantile regression is to perform analysis of the conditional quantile functions one percentile level at a time. This approach offers great modeling flexibility at the cost of statistical efficiency. The Principle Investigator proposes to develop and study new approaches to efficient modeling of conditional quantile functions. By "borrowing strength" across neighboring quantiles and utilizing a Bayesian empirical likelihood approach, the investigator aims to advance the theory, methodology, and applications of efficient quantile regression. Efficiency gain is an important consideration of any statistical research, and the proposed modeling techniques are especially helpful in the analysis of quantiles in the data-sparse areas. The Bayesian empirical likelihood approach for quantile regression can be used in conjunction with optimal weighting for semiparametric efficiency, and with Markov chain Monte Carlo sampling for effective computation in a high dimensional parameter space.The proposed models, to be called semi-local quantile models, strike to balance bias and variance; when the models do not hold exactly, the proposed estimators follow the spirit of regularization.Inference in data-sparse areas, including but not restricted to the analysis of high tails, is highly valuable in a wide range of scientific and social studies. The proposed research is motivated by the investigator's interdisciplinary research in climate studies and public health, and will provide researchers in statistics and other fields novel tools for better understanding and quantifying relationships between measurements. The proposed activities include new opportunities for graduate students to participate in transformative research, and will enable the investigator to continue integration of research with teaching and mentoring. The investigator pursues active academic exchanges through lecturers and collaborations, and free distribution of software, for broad dissemination of the research results.

近年来，分位数回归已成功成为对更常规的最小二乘回归的有力补充。通过对条件分位数进行建模，研究人员通常能够对响应变量与协变量如何相关的更全面地了解。分位数回归的主要方法是一次对条件分位数函数进行分析。这种方法以统计效率为代价提供了很好的建模灵活性。原则研究者建议开发和研究有条件分位功能的有效建模的新方法。通过“借用强度”跨越相邻的分位数并利用贝叶斯经验可能性方法，研究者旨在推进有效分位数回归的理论，方法和应用。效率增益是任何统计研究的重要考虑因素，所提出的建模技术对分析数据 - 帕克斯区域的分位数特别有用。分位数回归的贝叶斯经验可能性方法可以与最佳的半级效率一起使用，以及马尔可夫链链蒙特卡洛采样，以在高维参数空间中进行有效计算。拟议的模型，被称为半局部分位数模型，以平衡偏见和变异；当模型不完全成立时，提出的估计量遵循正规化的精神。在广泛的科学和社会研究中，数据 - 帕斯斯区域（包括但不限于对高尾巴进行分析）的参与非常有价值。拟议的研究是由研究者在气候研究和公共卫生中的跨学科研究的启发，并将为统计和其他领域的研究人员提供新颖的工具，以更好地理解和量化测量之间的关系。拟议的活动包括研究生参加变革性研究的新机会，并将使研究人员能够继续将研究与教学和指导整合。研究人员通过讲师和合作以及软件的自由分销来追求积极的学术交流，以广泛传播研究结果。