Statistical Methods for Dependent Data

这项建议侧重于与相关数据的统计分析有关的各种专题。第一个项目扩展了用于分析DNA序列的光谱包络概念。分析长DNA序列数据的一个常见问题是识别蛋白质编码序列，这些序列分散在整个序列中，并被非编码区隔开。DNA序列是异质性的，因此有必要扩展方法学以捕捉此类序列的局部行为。为了解决局部行为的问题，将探索一种局部谱包络，该包络通过混合平滑样条来进行估计。希望这种方法将有助于以快速和自动的方式强调存在于几乎任何长度的分类序列中的任何周期性特征。人类基因组计划等项目已经产生了大量数据，该项目中建立的方法将被证明在分析各种基因组计划产生的大量数据方面是有用的。在另一个项目中，重点是对纵向数据的分析和开发一个实用的非参数程序来估计受试者内部的相关结构。该技术被用来开发数据驱动的函数主成分分析程序(FPCA)。由于纵向数据通常具有受试者内部的观察结果相互关联的特性，因此需要对这些数据进行有效的分析来解释这种受试者内的相关性。当协方差结构的参数形式未知时，使用错误指定的结构可能会导致估计有偏差和效率低下。这个项目的重点是分析纵向数据，这些数据可以被建模为来自平滑受试者轨迹的观测，这些受试者轨迹是在离散时间点观察到的具有噪声的随机过程的实现。纵向数据的高维性和复杂性使得FPCA通过捕捉产生数据的随机过程的主要变化模式而成为数据约简和可视化的流行工具。科学家通常感兴趣的是使用纵向数据来确定一组可能随时间变化的协变量对给定响应随时间的影响。函数线性模型，特别是变系数模型，为分析此类数据提供了一个框架。在许多这样的数据集中，函数系数具有不能用参数建模的形状。需要对这些数据进行有效的分析，既要考虑到受试者内部的相关性，又要考虑到系数的灵活形状。由于受试者内部协方差的参数形式并不总是已知的，第三个项目专注于创建基于迭代数据驱动的基于样条法的过程来拟合变系数模型。这项建议集中于解决相关数据分析中涉及的问题。第一个项目将开发一种检测长DNA序列中基因的方法。人类基因组计划等项目已经产生了大量数据，该项目中建立的方法将被证明在分析各种基因组计划产生的大量数据方面是有用的。第二个拟议的项目侧重于分析一段时间以来收集的复杂数据。这个项目的动机也是DNA分析，特别是基因表达数据的分析。在第三个项目中，研究人员将专注于一种名为功能线性模型的技术。例如，将开发技术来研究在治疗卵巢癌时，生长因子对决定用抗血管生成疗法辅助化疗的影响。

This proposal concentrates on various topics relating to the statistical analysis of dependent data. The first project extends the spectral envelope concept for analyzing DNA sequences. A common problem in analyzing long DNA sequence data is in identifying protein-coding sequences that are dispersed throughout the sequence and separated by regions of noncoding. DNA sequences are heterogeneous, so it is necessary to expand the methodology to capture the local behavior of such sequences. To address the problem of local behavior, a local spectral envelope with estimation via mixtures of smoothing splines will be explored. It is the hope that this methodology will help emphasize any periodic 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 and the methods established in this project will prove to be useful in the analysis of the vast quantities of data being produced by various genome projects. In another project, the focus is on the analysis of longitudinal data and the development of a practical nonparametric procedure for the estimation of the within-subject correlation structure. This technique is used to develop a data driven functional principal components analysis procedure (FPCA). Because longitudinal data often possess the property that observations made within a subject are correlated, an effective analysis of these data is required to account for this within-subject correlation. When a parametric form for the covariance structure is unknown, using a misspecified structure can result in biased and inefficient estimates. This project focuses on the analysis of longitudinal data that can be modeled as observations from smooth subject trajectories that are realizations of a stochastic process observed at discrete time points with noise. The high dimensionality and complexity of longitudinal data has made FPCA a popular tool for data reduction and visualization by capturing the primary modes of variation of the stochastic process generating the data. Scientists are often interested in using longitudinal data to determine the effect that a set of possibly time-varying covariates have on a given response over time. Functional linear models, and in particular the varying-coefficient model, provide a framework for analyzing such data. In many of these data sets, the functional coefficients have shapes that cannot be modeled parametrically. An effective analysis of these data is required to both account for the within-subject correlation and to allow for the flexible shapes of the coefficients. Because a parametric form for the within-subject covariance is not always known, a third project focuses on creating an iterative data-driven spline based procedure for fitting varying-coefficient models. This proposal concentrates on solving problems involved in the analysis of dependent data. The first project will develop a method for detecting genes in a long DNA sequences. Projects such as the human genome project have produced large amounts of data and the methods established in this project will prove to be useful in the analysis of the vast quantities of data being produced by various genome projects. A second proposed project focuses on the analysis of complex data collected over time. This project is also motivated by the analysis of DNA, and in particular, the analysis of gene expression data. In a third project, the investigators will focus on a technique called functional linear models. For example, techniques will be developed for studying the effect that a growth factor should have on the decision to supplement chemotherapy with antiangiogenic therapy when treating ovarian cancer.