Estimation, model selection and inference in two classes of non- and semi-parametric models for repeated measurements

用于重复测量的两类非参数和半参数模型的估计、模型选择和推理

• 批准号: 1306972
• 负责人: Shujie Ma
• 金额: $ 9.99万
• 依托单位: University of California-Riverside
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-08-15 至 2016-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1306972&HistoricalAwards=false
• 关键词: Estimation; model; selection; inference; two

In this proposal, the PI plans to develop new non- and semi- parametric regression strategies in the context of repeated measures data with diverging number of covariates. The methods are supported by large sample theories. Specifically, the PI aims at: (1) developing efficient estimation and model selection procedures by incorporating the within-subject correlations in two proposed broad classes of models: a generalized varying index coefficient additive model and a generalized additive coefficient model. The PI proposes to employ a group penalized estimation method with polynomial splines; (2) proposing an oracally efficient and computationally expedient two-step spline estimation procedure for nonparametric additive functions. The proposed two-step estimator is proved to have the oracle efficiencies in terms of both model estimation and selection. Such superior properties are achieved by taking advantage of the joint asymptotics of spline functions with different smoothing parameters and regularization; (3) conducting statistical inferences after model selection. The PI proposes a new nonparametric inferential tool to test whether a nonparametric function has a given parametric form, and constructs simultaneous confidence bands to provide global inference of functions with their asymptotic properties established; and (4) studying model checking problems for the proposed structured models by an integrated conditional moment test.The proposal meets the immediate needs from various scientific areas for analyzing high dimensional repeated measures data within the non- and semi- parametric framework. The proposed research is motivated by the real data problems coming from the PI's interactions with researchers from different disciplines. The data applications include gene-environment and risk factor-environment interactions, nutrition scores, children growth, and economic growth problems. The completion of the proposed projects will greatly enhance the capability of researchers to analyze high-dimensional repeated measures data with more reliable, flexible and effective statistical methods. The research methods and results will be disseminated through journal publications, seminars, conferences and workshops, and they will be incorporated into a graduate course on longitudinal data analysis. Moreover, the project will promote teaching and training of undergraduate and graduate students on the state-of-the-art techniques in the research topics related to this proposal. The PI plans to provide practitioners with easy-to-implement and easy-to-interpret well-documented procedures coded in software such as R and to make the software packages available to the public.

在本提案中，PI计划在重复测量数据（协变量数量不同）的背景下开发新的非参数和半参数回归策略。该方法得到了大样本理论的支持。具体而言，PI的目标是：（1）通过将受试者内相关性纳入两大类模型（广义变指数系数加性模型和广义加性系数模型），开发有效的估计和模型选择程序。PI提出采用多项式样条的组惩罚估计方法;（2）提出了一个口头上有效的和计算方便的两步样条估计程序的非参数加性函数。证明了所提出的两步估计在模型估计和选择方面都具有预言效率。这种上级性质是通过利用具有不同光滑参数的样条函数和正则化的联合渐近性来实现的;（3）在模型选择之后进行统计推断。PI提出了一种新的非参数推理工具来检验非参数函数是否具有给定的参数形式，并构造了同时置信带来提供函数的全局推理，并建立了它们的渐近性质;以及（4）利用条件矩检验方法研究了结构化模型的模型检验问题，满足了各科学领域对高维分析的迫切需要在非参数和半参数框架内重复测量数据。拟议的研究是由来自PI的互动与来自不同学科的研究人员的真实的数据问题的动机。数据应用包括基因-环境和风险因素-环境相互作用、营养评分、儿童生长和经济增长问题。这些项目的完成将极大地提高研究人员用更可靠、更灵活、更有效的统计方法分析高维重复测量数据的能力。研究方法和结果将通过期刊出版物、研讨会、会议和讲习班传播，并将纳入关于纵向数据分析的研究生课程。此外，该项目将促进本科生和研究生在与本提案相关的研究课题中的最先进技术方面的教学和培训。PI计划为从业人员提供易于实施和易于解释的程序，这些程序用R等软件编码，并向公众提供软件包。