Collaborative Research: Integral Transform Methods for Sufficient Dimension Reduction in Regression

合作研究：回归中充分降维的积分变换方法

• 批准号: 0707004
• 负责人: Yu Michael Zhu
• 金额: $ 7.99万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-08-15 至 2010-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0707004&HistoricalAwards=false
• 关键词: Collaborative; Research; Integral; Transform; Methods

This project is aimed to develop theory and methods for sufficient dimension reduction in regression analysis involving a large number of predictor variables. The investigators propose a general approach called the integral transform approach to facilitating dimension reduction. The key idea of this approach is to use integral transform and response transformation to change the domain where dimension reduction is performed. Due to the availability of a wide range of transformations and integral transforms, this approach leads to a flexible and effective framework for addressing and resolving challenges raised by high dimensionality. Through a series of well-defined research problems, the investigators study this framework and develop specific dimension reduction methods for many important regression applications. The success of this project not only provides effective practical tools for high-dimensional data analysis but also represents an advance in the theory and methodology of semiparametric inference.High-dimensional data that involve a large amount of variables are nowadays routinely generated and collected in areas such as scientific research, government, business, etc. It is well-known that high dimensionality causes difficulties in processing and analyzing these data. This is commonly referred to as the curse of dimensionality. There is an urgent demand of statistical tools that are able to mitigate the curse of dimensionality through dimension reduction. This project represents an answer to this demand and is particularly aimed at achieving dimension reduction in regression. The results from this project can be widely applied in areas where regression involving a large number of variables is required. Gene expression and protein sequence data analysis is one such example. Therefore, this project can help enhance scientific research and discovery and benefit a variety of social and economical activities.

该项目的目的是开发涉及大量预测变量的回归分析中足够尺寸的理论和方法。研究人员提出了一种称为“积分转换方法”，以促进降低维度。这种方法的关键思想是使用积分转换和响应变换来改变执行尺寸降低的域。由于具有广泛的转换和整体转换的可用性，这种方法为解决和解决高维度提出的挑战提供了灵活有效的框架。通过一系列定义明确的研究问题，研究人员研究了该框架并为许多重要的回归应用开发了特定的缩小方法。该项目的成功不仅为高维数据分析提供了有效的实用工具，而且还代表了半参数推理的理论和方法的进步。如今，涉及大量变量的高维数据是在科学研究，政府，业务等领域常规生成和收集的。众所周知，这是众所周知的，这是众所周知的，这是高度损害的困难和分析，并分析了这些数据以及分析这些在这些数据中的分析。这通常称为维度的诅咒。统计工具的紧急需求能够通过降低维度来减轻维度的诅咒。该项目代表了这一需求的答案，尤其是旨在实现缩小回归的尺寸。该项目的结果可以广泛应用于需要大量变量的回归区域。基因表达和蛋白质序列数据分析就是这样一个例子。因此，该项目可以帮助增强科学研究和发现，并受益于各种社会和经济活动。