Model selection and efficient learning for high dimensional clustered data

本研究旨在为变量数大于样本量的复杂高维聚类数据发展统计理论和实用方法。这个问题在涉及数千个基因的微阵列数据中尤其重要和相关。这项研究的重点将是展示如何从由高维数据组成的大量经常是噪声的信息中高效和准确地提取信息，从而识别和选择具有科学意义的重要变量。PI和她的合作者将通过将相关性纳入模型来开发估计程序、统计推断功能、模型选择和分类程序。这一研究计划的具体目标是：(1)当广义线性模型中的链接函数和边际方差函数的形式未知时，提出灵活的估计方法；(2)发展时间过程基因表达数据的半参数分类；(3)提出选择信息相关结构的模型选择标准；(4)为似然性未知的广义加性模型发展有效且一致的模型选择程序；(5)开发一种充分的相关数据降维方法，在不强加参数模型的情况下保留完整的回归信息。该研究项目将有助于解决统计科学中的基本问题，并将激发一大批科学家对纵向和聚类数据分析领域的兴趣。它还将促进统计学、生物统计学和计算机科学的理论和方法的发展，并将它们联系起来。这项研究将在生物医学研究、基因组研究、计量经济学、环境研究、海洋学、社会科学和公共卫生等经常出现相关数据的领域产生重大影响和许多应用。国际统计研究所将通过开发新的大学课程和在主要统计会议上举办短期课程，将拟议的研究领域大量纳入教育活动。这项研究将促进本科生和研究生处理高维关联数据的学习和培训。

This research project is aimed at developing statistical theory and practical methodology for complex high-dimensional clustered data where the number of variables is larger than the sample size. This problem is especially important and relevant in microarray data where there are thousands of genes involved. The focus of this research will be to show how to efficiently and accurately extract information from a large quantity of often noisy information consisting of high-dimensional data, so as to identify and select significant variables of scientific interest. The PI and her collaborators will develop estimation procedures, statistical inference functions, model selection and classification procedures by incorporating correlation into the models. The specific goals for this research plan are: (1) To propose flexible estimation procedures for the link function and the marginal variance function when their forms are unknown in the generalized linear models; (2) To develop semiparametric classification for time-course gene expression data; (3) To propose model selection criteria for choosing informative correlation structures; (4) To develop efficient and consistent model selection procedures for generalized additive models where the likelihood is unspecified; (5) To develop a sufficient dimension reduction method for correlated data and retain the full regression information without imposing parametric models.The research project will help to tackle fundamental questions in statistical science and will stimulate interest from a large group of scientists in the fields of longitudinal and cluster data analysis. It will also enhance the development of, and makes connections between, theory and method in statistics, biostatistics and computer science. This research will have significant impact and many applications in biomedical studies, genome research, econometrics, environmental studies, oceanography, social science and public health where correlated data often arise. The PI will integrate the proposed research areas substantially into educational activities through the development of new university courses, and through presenting short courses at major statistical meetings. The research will advance undergraduate and graduate students' learning and training for handling high-dimensional correlated data.