Efficient Modeling in Quantile Regression

近年来，分位数回归作为传统最小二乘回归的有力补充而成功地出现。通过对条件分位数函数进行建模，研究人员通常能够更全面地了解响应变量如何与其协变量相关联。分位数回归中流行的方法是一次执行一个百分位数水平的条件分位数函数分析。这种方法以牺牲统计效率为代价提供了极大的建模灵活性。主要研究者建议开发和研究新的方法来有效地建模条件分位数函数。通过在相邻分位数之间“借用力量”并利用贝叶斯经验似然方法，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，所提出的建模技术特别有助于数据稀疏区域的分位数分析。分位数回归的贝叶斯经验似然方法可以与半参数有效性的最优加权和高维参数空间中有效计算的Markov chain Monte Carlo抽样相结合，所提出的模型称为半局部分位数模型，能够平衡偏差和方差;当模型不完全成立时，所提出的估计器遵循正则化的精神。在数据稀疏区域的推断，包括但不限于高尾分析，在广泛的科学和社会研究中非常有价值。拟议的研究是由调查员在气候研究和公共卫生的跨学科研究的动机，并将提供统计和其他领域的研究人员更好地理解和量化测量之间的关系的新工具。拟议的活动包括研究生参与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相结合。研究者通过讲师和合作以及免费分发软件来进行积极的学术交流，以广泛传播研究成果。

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.