Collaborative Research: Renyi Divergence-based Robust Inference in Regression, Time Series and Association Studies.

这个合作研究项目的重点是开发一种新的方法，以减少回归，时间序列和多元关联研究的基础上，一个家庭的雷尼分歧，与提供估计的中心主题是固有的强大的数据污染，维持只有最小的损失效率。该族不仅刻画了回归和时间序列中充分降维概念的条件独立性，而且刻画了多元关联研究中典型变量之间的独立性。该方法的新奇之处在于利用的家庭，它平衡的估计的效率和鲁棒性的程度的调整参数。在这三个领域的每一个，该项目的重点是调查一系列的问题，如：（i）估计的计算，（ii）检测的真实尺寸，（iii）选择一个最佳的调整参数，（iv）通过理论的方法的正式理由。此外，该项目的重点是通过影响函数和样本/经验影响函数对鲁棒性进行深入研究。最后，该项目的重点是找到一个最佳的Rényi散度度量，既鲁棒又有效，而不需要事先检测或删除离群值。技术的迅速发展导致了大多数科学的信息过载。许多当代数据集的一个典型特征是它们本质上是相对高维的。这促使应用科学转向回归，时间序列和多元关联中产生的不同关系研究流派，通常称为降维，其目标是减少变量的维度作为数据分析的第一阶段。然而，在高维数据集的离群值的存在下，现有的降维方法的性能产生不利影响，导致结论是不完全可靠的。由于离群值在高维数据集中经常遇到，并且它们的存在很难检测，因此迫切需要识别具有一定程度的自动鲁棒性或对离群值不敏感的降维方法。拟议的项目提供了强大的降维方法，这将大大有助于分析社会科学，机器学习，体育，经济学，环境研究，形态计量学和癌症研究等领域的高维数据。事实上，该项目不仅将为各个学科的科学家提供新的工具，以获得关于高维数据分析的可靠结论，而且还将显著推进统计理论，从而在降维方面开辟新的研究路径。

This collaborative research project focuses on developing a novel approach to dimension reduction in regression, time series, and multivariate association studies based on a family of Rényi divergences, with a central theme of providing estimators that are inherently robust to data contamination, sustaining only a minimal loss in efficiency. This family not only characterizes the conditional independence underlying the concept of sufficient dimension reduction in regression and time series, but also characterizes independence between canonical variates in multivariate association studies. The novelty of the approach lies in exploiting a tuning parameter of the family, which balances the efficiency and the degree of robustness of the estimators. In each of the three areas, this project focuses on investigating a host of issues such as: (i) the computation of estimates, (ii) the detection of the true dimension, (iii) the selection of an optimal tuning parameter, and (iv) a formal justification of the method via theory. Furthermore, the project focuses on carrying out an in-depth study of robustness via influence functions and sample/empirical influence functions. Finally, the project focuses on finding an optimal Rényi divergence measure that is both robust and efficient, without the need for prior outlier detection or removal. Rapid advances in technology have led to an information overload in most sciences. A typical characteristic of many contemporary datasets is that they are relatively high-dimensional in nature. This has prompted a shift in the applied sciences toward a different relationship-study genre arising in regression, time series and multivariate association, popularly known as dimension reduction, whose goal is to reduce the dimensionality of the variables as a first phase in the data analysis. However, the presence of outliers in high-dimensional datasets adversely affects the performance of existing dimension reduction methodologies, resulting in conclusions that are not completely reliable. Given that outliers are commonly encountered in high-dimensional datasets and that their presence is hard to detect, there is an urgent need to identify dimension reduction methods that possess some degree of automatic robustness, or non-sensitivity, to outliers. The proposed project provides robust dimension reduction methods, which would contribute significantly to the analysis of high-dimensional data arising in fields such as the social sciences, machine learning, sports, economics, environmental studies, morphometrics and cancer studies, among others. In fact, this project will not only provide novel tools for scientists in various disciplines to obtain reliable conclusions on high-dimensional data analysis, but also significantly advance the statistical theory, thereby paving a new research path in dimension reduction.