Collaborative Research: Penalization Methods for Screening, Variable Selection and Dimension Reduction in High-Dimensional Regression via Multiple Index Models

该项目旨在开发有效的惩罚方法，用于高维回归中的筛选、降维和变量选择。研究人员主要关注多指标模型，因为这类模型结合了线性回归和非参数回归的优点，同时避免了它们的缺点。采用一种新的惩罚方法进行模型拟合，对多指标模型的参数分量和非参数分量进行正则化。一项初步研究表明，这种方法比现有的其他方法更具优势。当面对超高维度时，调查人员使用正向变量筛选程序将维度降低到可管理的大小，然后应用拟议的惩罚。研究人员计划研究这种方法的理论性质，并为其实施开发快速高效的计算算法。科学技术的进步导致了生物信息学、气候研究、互联网等领域海量数据的爆炸性增长，传统的统计方法在处理大量变量时变得不再有效。最近，大量的研究工作致力于发展统计方法，如降维和变量选择，以分析这类海量数据。研究人员提出了一种新的惩罚方法，并开发了高效的计算算法，从而加入了这一努力。该项目的成果不仅促进了统计研究，而且有助于其他科学家和研究人员更好地理解和分析他们的海量数据，从而提高他们的科学发现。

The project aims to develop effective penalization methods for screening, dimension reduction, and variable selection in high dimensional regression. The investigators focus mainly on multiple index models, because this type of models combines the strengths of linear and nonparametric regression while avoiding their drawbacks. A novel penalization approach is employed for model fitting, which regularizes both the parametric and nonparametric components of a multiple index model. A pilot study shows that this approach is more advantageous than other existing ones. When facing ultra-high dimensionality, the investigators use a forward variable screening procedure to reduce the dimension to a manageable size before applying the proposed penalization. The investigators plan to study the theoretical properties of this approach and develop fast and efficient computing algorithms for its implementation. The proposed approach is further extended to applications involving categorical responses or random effects.Advances in science and technology have led to an explosive growth of massive data across a variety of areas such as bioinformatics, climate research, internet, etc. Traditional statistical methods for clustering, regression and classification become ineffective when dealing with a large number of variables. Lately, a tremendous amount of research effort has been dedicated to the development of statistical methods such as dimension reduction and variable selection for analyzing this type of massive data. The investigators join the effort by proposing a novel penalization approach and developing efficient computing algorithms. The results from this project not only advance statistical research but also help other scientists and researchers better understand and analyze their massive data and hence enhance their scientific discovery.