Sufficient Dimension Reduction for Missing, Censored, and Correlated Data

针对缺失、删失和相关数据进行充分降维

• 批准号: 0706919
• 负责人: Lexin Li
• 金额: $ 11.99万
• 依托单位: North Carolina State 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: 2007-09-15 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0706919&HistoricalAwards=false
• 关键词: Sufficient; Dimension; Reduction; Missing; Censored

This proposal aims to develop new theory and methodology for sufficient dimension reduction (SDR). In particular, the research focuses on biostatistical problems which commonly include missing data, survival data, and longitudinal data analysis. The proposed methodology can effectively transform a high dimensional regression problem to a low dimensional projection, retain full regression information, and impose few or no probabilistic models. There are three components to this research. First, the investigator proposes a family of augmented inverse probability weighted SDR estimators when predictors have missing observations. This new approach allows a more general missing data mechanism than the existing solution and permits more flexible regression forms beyond the homoscedastic linear model. The second component of the research targets SDR for survival data, where the response of time to death or disease recurrence is subject to censoring. Viewing the censored response as a specific type of missing data, the investigator integrates an inverse probability weighted estimation strategy with a variety of SDR methods. Thirdly, the investigator studies a type of longitudinal data where measurements for all the study subjects are collected at the same scheduled time points. Both a population foundation and the associated estimation procedure are developed. All three components center around commonly encountered biostatistical problems and the development of the three components are interrelated.Modern technologies have pushed the frontier of science with the capability of generating and collecting data in large quantity and high dimensionality. Examples of large high dimensional data sets arise in a great number of research areas, such as environmental studies, human health and medical research, and homeland security. Sufficient dimension reduction (SDR) methodology effectively transforms a high dimensional data problem to a low dimensional one. Consequently, SDR allows many existing analytical methods, which used to be hindered by the curse of dimensionality, to now work for the high dimensional problems. In addition, informative visualization of the data often becomes possible after dimension reduction, facilitating both the understanding and the analysis of the data. By developing new theory and methodology for missing, censored, and correlated data, the investigator's research extends the boundary of SDR to biostatistics as well as other disciplines such as econometrics, finance and bioinformatics. The impact of this research is anticipated to be widespread, due to the prevalence of the high dimensional data and the urgent demand for effective analytical tools to tackle those problems.

该提案旨在开发新的理论和方法，以减少维度（SDR）。特别是，研究的重点是生物统计问题，这些问题通常包括缺少数据，生存数据和纵向数据分析。所提出的方法可以有效地将高维回归问题转化为低维投影，保留完整的回归信息，并施加很少或没有概率模型。这项研究有三个组成部分。首先，研究者提出一个增加的逆概率加权SDR估计量的家族，当预测因子缺少观察结果时。这种新方法允许比现有解决方案更普遍地缺少数据机制，并允许超出同型线性线性模型以外的更灵活的回归形成。研究的第二个成分针对SDR的生存数据，其中时间对死亡或疾病复发的响应是对审查的。研究人员将审查的响应视为特定类型的缺少数据类型，将逆概率加权估计策略与多种SDR方法集成在一起。第三，研究者研究了一种纵向数据，其中所有研究对象的测量是在相同的计划时间点收集的。制定了人口基础和相关的估计程序。这三个组件围绕着通常遇到的生物统计问题，并且这三个组成部分的开发是相互关联的。现代技术已经推动了科学的边界，具有大量生成和收集数据的能力。大量高维数据集的示例在许多研究领域中出现，例如环境研究，人类健康和医学研究以及国土安全。足够的尺寸降低（SDR）方法有效地将高维数据问题转化为低维数据。因此，SDR允许许多现有的分析方法，这些分析方法过去被维度的诅咒阻碍，现在可以解决高维问题。此外，在降低维度后，通常可以看到数据的信息，从而促进了对数据的理解和分析。通过为缺失，审查和相关数据开发新的理论和方法，研究者的研究将SDR的边界扩展到生物统计学以及其他学科以及计量经济学，金融和生物信息学等其他学科。由于高维数据的普遍性以及对解决这些问题的有效分析工具的迫切需求，这项研究的影响预计将是普遍的。