Semiparametric Inference for High-dimensional Correlated or Heterogeneous Cross-sectional Data with Discrete Response

具有离散响应的高维相关或异构横截面数据的半参数推理

• 批准号: 1007603
• 负责人: Lan Wang
• 金额: $ 17.66万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-01 至 2013-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1007603&HistoricalAwards=false
• 关键词: Semiparametric; Inference; dimensional; Correlated; Heterogeneous

Substantial advancement has been achieved over the past decade in high-dimensional data analysis with diverging number of covariates. However, when the research interest is focused on modeling the relationship between the response variable and a high-dimensional vector of covariates, most existing work only applies when the response variable is continuous and often requires stringent conditions such as independence or homogeneity. Many fundamental problems remain unsolved for high-dimensional data with discrete responses, especially when the standard modeling assumptions are not satisfied. This project aims to develop new statistical theory, methodology and algorithms for analyzing high-dimensional correlated or heterogeneous cross-sectional data with binary or count responses. More specifically, the investigator will (1) rigorously study the asymptotic theory, including consistency and asymptotic normality, of the semiparametric procedure of generalized estimating equations in the new diverging p asymptotic framework; (2) investigate generalized estimating equations based variable selection procedures for high-dimensional longitudinal and spatially correlated data; and (3) investigate the theory and methodology of sparse quantile regression, where the number of parameters may greatly exceed sample size, for analyzing heterogeneous data with possibly discrete responses.The prevalence of high-dimensional binary and count data in various scientific fields, such as biomedical and health sciences, economics, social sciences and environmental studies, demands new statistical theory, methodology and software. Many important issues in analyzing high-dimensional binary or count data, especially in the presence of correlation or heterogeneity, have not been systematically studied. Moreover, existing work based on the full likelihood or the independence assumption in the high-dimensional setting cannot be readily applied. This project will make significant and timely contribution to the general theory and methodology of high-dimensional data analysis in the diverging p framework. Such theories are critical for guiding practical data analysis. Undergraduate and graduate students, especially those from underrepresented groups, will be encouraged to participate in this research project.

在过去的十年中，在高维数据分析中已经取得了实质性的进展，不同数量的协变量。然而，当研究兴趣集中在响应变量和协变量的高维向量之间的关系建模时，大多数现有的工作仅适用于响应变量是连续的，并且通常需要严格的条件，如独立性或同质性。对于具有离散响应的高维数据，许多基本问题仍未解决，特别是当标准建模假设不满足时。本项目旨在开发新的统计理论、方法和算法，用于分析具有二元或计数响应的高维相关或异质横截面数据。 更具体地说，研究者将（1）在新的发散p渐近框架下严格研究广义估计方程的半参数过程的渐近理论，包括一致性和渐近正态性;（2）研究基于广义估计方程的高维纵向和空间相关数据的变量选择过程;（3）研究参数数目可能大大超过样本容量的稀疏分位数回归的理论和方法，用于分析具有可能离散响应的异质数据。如生物医学和卫生科学、经济学、社会科学和环境研究等领域的统计学研究需要新的统计理论、方法和软件。在分析高维二进制或计数数据时，特别是在相关性或异质性存在的情况下，许多重要问题尚未得到系统的研究。此外，现有的工作的基础上的充分的可能性或独立性假设在高维设置不能很容易地应用。本项目将对发散p框架下高维数据分析的一般理论和方法做出重要而及时的贡献。这些理论对于指导实际数据分析至关重要。本科生和研究生，特别是那些来自代表性不足的群体，将被鼓励参加这个研究项目。