Collaborative Research: The Analysis of Time Series Collected in Experimental Designs

协作研究：实验设计中收集的时间序列分析

• 批准号: 0706709
• 负责人: Hernando Ombao
• 金额: $ 4.3万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-07-01 至 2007-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0706709&HistoricalAwards=false
• 关键词: Collaborative; Research; Analysis; Time; Series

The research project has three basic goals. The first goal is to estimate the second order properties of a nonstationary process using data from multiple units. A wavelet-based functional model with stochastic subject-specific representation is proposed. A computationally efficient algorithm for estimation will be developed along with theoretical optimal properties of the estimators. While this project is focused on the frequency or spectral domain, the second project will develop methods in the time domain. The goal of this project is to accommodate structural breaks within the time series using mixtures of state-space models. These mixtures are characterized by covariates, treatment and subject-specific effects in both the mixture components and mixing weights. The third project focuses on both temporal and spatial components. In particular, this project integrates spatial information by developing models and corresponding estimators to accommodate data structures in both time and space. The goal is to assess the differences across groups and the subject-specific and covariate effects on the dynamic structure.The research focuses on an area that has been, for the most part, neglected by the statistics community. In particular, the question to be addressed is how to best analyze data obtained from experiments when the data are taken sequentially in time and/or space. Typical examples include experiments where EEGs are taken on various subjects with different diagnoses, or functional magnetic resonance imaging (fMRI) experiments, where subjects with different conditions are requested to perform tasks while in a magnet. The difficulty in analyzing such data is that they are often irregular (nonhomogeneous or nonstationary) in nature. The techniques for analyzing regular time series are well established, but new techniques are needed to account for the irregularities over time and/or space. The fact that these data are collected in complex experiments adds another layer of difficulty onto the analysis.

研究项目有三个基本目标。第一个目标是使用来自多个单元的数据估算非平稳过程的二阶属性。提出了具有随机主题特异性表示的基于小波的功能模型。将开发一种用于估计的计算有效算法以及估计器的理论最佳特性。尽管该项目集中在频率或光谱域上，但第二个项目将在时域中开发方法。该项目的目的是使用状态空间模型的混合物在时间序列中适应结构中断。这些混合物的特征是在混合物组件和混合重量中的协变量，治疗和受试者特异性效应。第三个项目侧重于时间和空间成分。特别是，该项目通过开发模型和相应的估计器来整合空间信息，以适应时间和空间中的数据结构。目的是评估群体之间的差异以及对动态结构的特定主题和协变量的影响。该研究重点是统计界忽略的领域。 特别是，要解决的问题是如何在时间和/或空间中顺序获取数据时如何最佳分析从实验中获得的数据。 典型的例子包括对具有不同诊断的各种受试者或功能磁共振成像（fMRI）实验进行脑电图的实验，其中要求具有不同条件的受试者在磁铁中执行任务。分析此类数据的困难在于它们在本质上通常是不规则的（非均匀或非统一的）。 分析常规时间序列的技术已经确定，但是需要新技术来解释随着时间和/或空间的不规则性。 这些数据是在复杂实验中收集的事实，这在分析中增加了另一层难度。