Statistical Methods in the Frequency Domain

频域统计方法

基本信息

  • 批准号:
    0102511
  • 负责人:
  • 金额:
    $ 27万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2001
  • 资助国家:
    美国
  • 起止时间:
    2001-07-01 至 2004-06-30
  • 项目状态:
    已结题

项目摘要

Abstract DMS-0102511 Stoffer & OmbaoIn this proposal, we concentrate on topics relating, in general, to statistical methods in the frequency domain. First, we propose to extend the spectral envelope methodology for stationary time series to the notion of evolutionary spectral envelope for nonstationary series. In another project, we will direct our attention to analyzing nonstationary multiple time series and their principal components using transforms based on smooth localized complex exponentials (SLEX). In a third project, we will consider spectral analysis of time series collected in experimental designs with covariates. The spectral envelope was first proposed as a method to analyze stationary categorical-valued time series in the frequency domain. The motivation for that research was the analysis of DNA sequences. A common problem in analyzing long DNA sequence data is in identifying coding sequences that are dispersed throughout the sequence and separated by regions of noncoding. It is well known that DNA sequences are heterogeneous, and even within short subsequences of DNA, one encounters local behavior. In this project, we are interested in extending the spectral envelope methodology to capture the local behavior of such sequences. To address this problem of local behavior in categorical-valued time series, we will explore using the spectral envelope in conjunction with a dyadic tree-based adaptive segmentation (TBAS) method for analyzing locally stationary processes. Our hope is that this methodology will help emphasize any harmonic feature that exists in a categorical sequence of virtually any length in a quick and automated fashion. Projects such as the human genome project have produced large amounts of data. We believe our methods will prove to be useful as a data mining technique for help in the analysis of the vast quantities of data being produced by various genome projects. While the first project focuses on Fourier based methods, the second project concentrates on other techniques that will give spatial (or time) and frequency localization. Our goal, as always, is to develop computationally efficient algorithms for the analysis of large data sets. In our initial investigations, we will focus on the SLEX transform for analyzing categorical-valued nonstationary time series, but our goal is eventually to apply the technique to multiple time series (and their principal components) in general. The SLEX transform has special properties that make it ideal for analysis of nonstationary time series. The SLEX transform is based on the SLEX basis functions which are localized in both the time and frequency domains. The SLEX transform yields a decomposition in both time and frequency and allows a choice among many orthogonal transforms. Orthogonality leads to computationally efficient procedures for automatic segmentation of nonstationary time series and will hopefully facilitate in our investigation of the theoretical elements of our proposed methodology. An orthogonal representation allows one to store the coefficients and later process them by methods such as nonlinear thresholding. Our feeling is that if the data can be reduced to a relatively small number of meaningful coefficients then these coefficients might be useful in some type of secondary statistical analysis. In our collaborations with other scientists and physicians, we frequently encounter settings where time series, and covariates, are recorded for several subjects in an experimental design. There is an absence of a core of statistical procedures for analyzing such data, and we typically run across techniques that are cooked up in an ad hoc manner by researchers who have little technical skill or knowledge for analyzing correlated data and estimating (spectral) functions. Our goal in this project is to develop a general, user friendly, statistical methodology that will incorporate the relevant information obtained from time series data sets recorded from several units from many groups, and where covariates may also be measured. Our initial approach will be to exploit the relationship between spectral density estimation and generalized linear models.
摘要DMS-0102511 Stoffer Ombao在本提案中,我们集中讨论与频域统计方法有关的主题。首先,我们建议扩展平稳时间序列的谱包络方法的概念演变谱包络的非平稳序列。 在另一个项目中,我们将把我们的注意力集中在分析非平稳多个时间序列及其主成分使用基于平滑局部复指数(SLEX)的变换。在第三个项目中,我们将考虑对在具有协变量的实验设计中收集的时间序列进行谱分析。 谱包络首先被提出作为一种在频域中分析平稳分类值时间序列的方法。这项研究的动机是分析DNA序列。 分析长DNA序列数据的一个常见问题是识别分散在整个序列中并被非编码区域分隔的编码序列。众所周知,DNA序列是异质的,即使在DNA的短序列中,也会遇到局部行为。 在这个项目中,我们有兴趣扩展频谱包络的方法来捕捉这种序列的本地行为。为了解决分类值时间序列中的局部行为问题,我们将探索使用谱包络结合基于二元树的自适应分割(TBAS)方法来分析局部平稳过程。我们的希望是,这种方法将有助于强调任何谐波特征,存在于一个分类序列的几乎任何长度在一个快速和自动化的方式。像人类基因组计划这样的项目已经产生了大量的数据。我们相信,我们的方法将被证明是有用的,作为一种数据挖掘技术,帮助分析大量的数据正在产生的各种基因组计划。虽然第一个项目侧重于基于傅立叶的方法,第二个项目集中在其他技术,将提供空间(或时间)和频率定位。我们的目标,一如既往,是为大型数据集的分析开发计算效率高的算法。在我们最初的研究中,我们将专注于分析分类值非平稳时间序列的SLEX变换,但我们的目标是最终将该技术应用于一般的多个时间序列(及其主成分)。SLEX变换具有特殊的性质,使其成为分析非平稳时间序列的理想方法。 SLEX变换基于在时域和频域中局部化的SLEX基函数。SLEX变换产生时间和频率的分解,并允许在许多正交变换中进行选择。非线性导致计算效率的程序自动分割的非平稳时间序列,并有望促进我们的调查,我们提出的方法的理论要素。正交表示允许存储系数并随后通过诸如非线性阈值化的方法来处理它们。我们的感觉是,如果数据可以减少到一个相对较少的有意义的系数,那么这些系数可能是有用的,在某种类型的二次统计分析。 在我们与其他科学家和医生的合作中,我们经常遇到在实验设计中记录多个受试者的时间序列和协变量的设置。没有一个核心的统计程序来分析这些数据,我们通常会遇到一些技术,这些技术是由研究人员以特别的方式炮制出来的,他们几乎没有技术技能或知识来分析相关数据和估计(谱)函数。 在这个项目中,我们的目标是开发一个通用的,用户友好的,统计方法,将纳入相关信息从时间序列数据集记录从几个单位从许多群体,其中协变量也可以测量。 我们最初的方法是利用谱密度估计和广义线性模型之间的关系。

项目成果

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David Stoffer其他文献

David Stoffer的其他文献

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{{ truncateString('David Stoffer', 18)}}的其他基金

Nonlinear and Nonstationary Time Series
非线性和非平稳时间序列
  • 批准号:
    1506882
  • 财政年份:
    2015
  • 资助金额:
    $ 27万
  • 项目类别:
    Continuing Grant
Statistical Methods for Dependent Data
相关数据的统计方法
  • 批准号:
    0805050
  • 财政年份:
    2008
  • 资助金额:
    $ 27万
  • 项目类别:
    Continuing Grant
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:
    0706723
  • 财政年份:
    2007
  • 资助金额:
    $ 27万
  • 项目类别:
    Standard Grant
Time Series Analysis and Applications
时间序列分析与应用
  • 批准号:
    0405038
  • 财政年份:
    2004
  • 资助金额:
    $ 27万
  • 项目类别:
    Continuing Grant
Expanding the Spectral Envelope
扩展光谱包络
  • 批准号:
    9703720
  • 财政年份:
    1997
  • 资助金额:
    $ 27万
  • 项目类别:
    Continuing Grant
The Spectral Envelope
光谱包络
  • 批准号:
    9404343
  • 财政年份:
    1994
  • 资助金额:
    $ 27万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Walsh-Fourier Analysis and Categorical Time Series
数学科学:沃尔什-傅里叶分析和分类时间序列
  • 批准号:
    9000522
  • 财政年份:
    1990
  • 资助金额:
    $ 27万
  • 项目类别:
    Standard Grant

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Computational Methods for Analyzing Toponome Data
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