Nonparametric and Semiparametric Models for High-Dimensional Data

摘要DMS-0204869 PI：Hans-Georg Mueller标题：高维数据的非参数和半参数模型研究者将专注于统计模型，理论，算法和应用，面向高维数据，特别是功能数据的分析。半参数方法是特别适合于这样的数据，因为通常很少知道这些数据的结构，而在同一时间的降维步骤是必要的，以避免“灾难的尺寸”。因此，通过拟合单指数或多指数模型，或通过截断函数数据扩展中包含的项的数量，以预测的形式降维是本项目的主要重点。这个项目的另一个重点是统计方法，考虑到曲线数据往往是随机曲线，受到个别不同的时间尺度。这导致了模型，理论，方法和算法的功能数据的时间弯曲。曲线数据在遗传学中是丰富的，其中基因表达谱的传播是最感兴趣的，并且在衰老和死亡率领域也是如此。研究者将开发功能回归、相关、判别和聚类分析的方法。这些方法将提供建立随机函数之间关系的工具，并允许将观察到的样本曲线分为不同的类别，在科学和其他实验和观察研究中收集的越来越复杂的大型数据通常可以被视为曲线或函数。这样的数据往往包含有价值的信息的时间动力学的物理和生物现象，并需要先进的统计技术来提取它。例如，记录重复的cDNA表达数据与基因微阵列可能包含有价值的信息的动态基因激活模式和基因调控。这些数据发挥重要作用的其他例子涉及生殖和衰老之间的关系，衰老和寿命的动态结构，或连续记录的各种血液蛋白质之间的关系。研究者将开发专门用于分析和解释此类数据的统计方法和模型。

AbstractDMS-0204869PI: Hans-Georg MuellerTitle: Nonparametric and Semi-parametric Models for High Dimensional DataThe investigator will focus on statistical models, theory, algorithms and applications geared towards the analysis of high-dimensional and in particular functional data. Semiparametric methods are particularly appropriate for such data since usually little is known about the structure of these data, while at the same time a dimension reduction step is necessary in order to avoid the "curse of dimension". Dimension reduction in the form of projections by fitting single index or multiple index models, or by truncating the number of terms included in an expansion of functional data, is therefore a major emphasis of this project. Another emphasis of this project are statistical methods that take into account that curve data often are random curves that are subject to individually varying time scales. This leads to models, theory, methodology and algorithms for time warping of functional data. Curve data are abundant in genetics where dissemination of gene expression profiles is of highest interest and also in the field of aging and mortality. The investigator will develop methods for functional regression, correlation, discriminant and cluster analysis. These methods will provide tools to establish relationships between random functions and allow classification of observed sample curves into distinct categories.Large and increasingly complex data that are being collected in scientific and other experimental and observational studies are often data that may be viewed as curves or functions. Such data often contain valuable information about the time-dynamics of physical and biological phenomena, and advance statistical techniques are needed to extract it. For example, recordings of repeated cDNA expression data with genetic microarrays may contain valuable information about the dynamics of gene activation patterns and gene regulation. Other examples where such data play a major role concern the relationship between reproduction and aging, the dynamic structure of aging and longevity, or the relationship between various blood proteins that are recorded continuously. The investigator will develop statistical methods and models specifically designed for the analysis and interpretation of such data.