Function estimation for biased sampling and fMRI data

有偏采样和功能磁共振成像数据的函数估计

• 批准号: 0707090
• 负责人: Kinh Truong
• 金额: $ 20万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-07-01 至 2011-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0707090&HistoricalAwards=false
• 关键词: Function; estimation; biased; sampling; fMRI

The proposal has three projects that involve the use of polynomial splines to model (1) point process and spatial-temporal time series, (2) selection biased (length-biased), and (3) randomly truncated data. The first part of Project (1) considers a linear regression model in which the response is a stationary time series and the explanatory series is a convolution of a point process and an unknown smooth function. The aim is to estimate the unknown smooth function. The second part of (1) deals with a non-parametric likelihood based approach to independent component analysis (ICA) by estimating the marginal distributions of the blind sources and the mixing matrix using the log-spline methodology. One of the advantages of the proposed procedure is the flexibility for incorporating the temporal or spatial correlation of the sources. The aim of Project (2) is to estimate the underlying density or conditional density function using selection-biased samples, by paying special attention to the situation in which the biased sampling density tends to zero at certain rates. To what extent this will affect the performance of the spline-based estimator is an important question and the investigator proposes to address it by examining the rates of convergence of the estimator. The last project deals with the estimation of density and conditional density functions involving randomly truncated data. A new methodology based on polynomial splines is proposed and software for the methodology will be developed. This methodology is important for examining a wide range of selection-bias or under-detection limits problems. Specifically, one can study the truncation pattern closely, especially when the information about how certain type of truncation might have occurred is available. Sampling properties of the spline-based estimators proposed in this grant application will be studied by extending the asymptotic results established previously by the investigator and his colleagues. Specifically, optimal rates of convergence and local asymptotics of the proposed estimates will be investigated and issues related to high-dimensional explanatory variables will also be addressed.This proposal has several broader impacts on applications to research in life sciences. First, the time series regression models and the approach to spatial-temporal data have a significant impact on brain research involving fMRI data, the proposed procedures are (a) less-biased, (b) capable to display the spatial-temporal information effectively, and (c) mathematically tractable in terms of statistical sampling properties. Second, the proposed unified approach to selection-biased or randomly truncated data provides major insights to the scientific community into the issues related to data acquisition. Robust statistical techniques are essential in the quest for important information from brain and genomic data. Third, methods proposed here will be useful for developing a course in statistical fMRI analysis to graduate students. Finally, a much broader health significance of this project will be its contribution to the better understanding of diseases that affect human lives.

该提案包含三个项目，涉及使用多项式样条来建模（1）点过程和时空时间序列，（2）选择偏差（长度偏差）和（3）随机截断数据。项目（1）的第一部分考虑线性回归模型，其中响应是平稳时间序列，解释序列是点过程和未知平滑函数的卷积。目的是估计未知的平滑函数。 (1) 的第二部分涉及基于非参数似然的独立分量分析 (ICA) 方法，通过使用对数样条方法估计盲源和混合矩阵的边际分布。所提出的程序的优点之一是能够灵活地合并源的时间或空间相关性。项目（2）的目的是使用有选择偏差的样本来估计基础密度或条件密度函数，特别注意有偏差的抽样密度在一定速率下趋于零的情况。这将在多大程度上影响基于样条的估计器的性能是一个重要问题，研究人员建议通过检查估计器的收敛率来解决这个问题。最后一个项目涉及涉及随机截断数据的密度和条件密度函数的估计。提出了一种基于多项式样条的新方法，并将开发该方法的软件。这种方法对于检查各种选择偏差或检测限不足的问题非常重要。具体来说，人们可以仔细研究截断模式，特别是当可以获得有关某种类型的截断如何发生的信息时。本拨款申请中提出的基于样条的估计量的采样特性将通过扩展研究者和他的同事先前建立的渐近结果来研究。具体来说，将研究所提议估计的最佳收敛率和局部渐近，并且还将解决与高维解释变量相关的问题。该提议对生命科学研究的应用具有更广泛的影响。首先，时间序列回归模型和时空数据方法对涉及功能磁共振成像数据的大脑研究具有重大影响，所提出的程序（a）偏差较小，（b）能够有效地显示时空信息，（c）在统计采样特性方面在数学上易于处理。其次，所提出的针对选择偏差或随机截断数据的统一方法为科学界提供了对数据采集相关问题的重要见解。强大的统计技术对于从大脑和基因组数据中获取重要信息至关重要。第三，这里提出的方法将有助于为研究生开发统计功能磁共振成像分析课程。最后，该项目更广泛的健康意义将在于它有助于更​​好地了解影响人类生活的疾病。