Feature and Structure Identification and Variable Selection for Functional, Longitudinal and Cross-sectional Data

该奖项是根据2009年《美国复苏和再投资法案》(公法111-5)提供资金的。在函数线性回归模型中，研究人员提出了一种特征识别方法来识别函数系数的零区间，并估计非零区间上的函数系数。这一过程可以看作是功能设置中的变量选择和降维。在纵向数据的广义线性模型中，研究人员提出了一种结构识别方法来选择聚集数据的相关结构。这种方法不需要似然函数，不受聚类大小的限制，而现有的大多数纵向数据处理方法都存在聚类规模大的问题，可以扩展到空间统计和基因网络。用于识别特征和结构的拟议估计器预计将享有甲骨文属性。为了考虑横断面数据的异质性，研究人员提出了变系数指数模型，包括了目前文献中的大多数变系数模型作为特例。在这种一般情况下，变量的选择是通过利用B-样条对非参数分量的逼近和采用概念上简单的典型相关优化来实现的。该提案有望继承降维技术的优良特性。研究人员的提案是由一项老化研究推动的，并扩展到地球科学、健康研究和生物信息学，以解决重要的科学问题。研究人员的工作旨在扩大函数回归模型和变系数指数模型的适用性，并在各种应用中更好地处理时间依赖回归分析。这项拟议的工作是第一批用坚实的渐近理论来解决所调查问题的方法论开发工作之一。调查人员计划向学术和工业用户提供拟议程序的免费软件包。这项拟议研究的支持有助于调查人员对弗吉尼亚大学的学生进行培训，那里几乎没有资深教职员工来监督大量的研究生，包括女性和少数族裔学生。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). In the functional linear regression model, the investigator proposes a feature identification procedure to identify the null intervals of the functional coefficients and to estimate the functional coefficients on the non-null intervals. This procedure can be considered as variable selection and dimension reduction in the functional setting. In the generalized linear model for longitudinal data, the investigator proposes a structure identification procedure to select the correlation structure for clustered data. This procedure does not require a likelihood function, is not restricted by cluster size while most existing methods for longitudinal data suffer from large cluster size, and can be extended to spatial statistics and gene networks. The proposed estimators for identifying features and structures are expected to enjoy the Oracle property. To account for heterogeneity in cross-sectional data, the investigator proposes the varying-coefficient index models, including most varying-coefficient models in the current literature as special cases. Variable selection is proposed in this general setting by utilizing B-spline approximations to the nonparametric components and adopting a conceptually simple optimization of canonical correlation. The proposal is expected to inherit nice properties from dimension reduction techniques.The investigator's proposal is motivated by an aging study, and has the extension to geosciences, health study, and bioinformatics for addressing important scientific questions. The investigator's work aims to broaden the applicability of functional regression models and varying-coefficient index models, and to enable better handling of time-dependent regression analysis in a variety of applications. The proposed work is among the first in methodology development with a solid asymptotic theory to address the investigated problems. The investigator has the plan to provide free software packages to academic and industrial users of the proposed procedures. The support of the proposed research helps the investigator in the training of the students at the University of Virginia, where few senior faculty members are available to supervise a larger number of graduate students, including female and minority students.