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）资助的。在函数线性回归模型中，研究者提出了一种特征识别方法来识别函数系数的零区间，并在非零区间上估计函数系数。这个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，研究者提出了一种结构识别程序来选择聚类数据的相关结构。该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方法都存在大聚类大小的问题，并且可以扩展到空间统计和基因网络。预计用于识别特征和结构的拟议估算器将享受Oracle属性。为了解释横截面数据的异质性，研究者提出了变系数指数模型，包括当前文献中的大多数变系数模型作为特殊情况。在这种一般情况下，通过对非参数成分利用b样条近似和采用典型相关的概念简单优化，提出了变量选择。该方案有望继承降维技术的优良特性。研究者的提议是由一项衰老研究激发的，并延伸到地球科学、健康研究和生物信息学，以解决重要的科学问题。研究者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，并使在各种应用中更好地处理时变回归分析。提出的工作是其中的第一个方法发展与坚实的渐近理论，以解决所调查的问题。研究者计划提供免费的软件包给学术和工业用户。对拟议研究的支持有助于研究者对弗吉尼亚大学学生的培训，在弗吉尼亚大学，很少有高级教师可以监督大量的研究生，包括女性和少数民族学生。

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.