Nonparametric and Semiparametric Models for High-Dimensional Data

【摘要】Hans-Georg mueller题目：高维数据的非参数和半参数模型。研究方向为高维数据特别是功能数据分析的统计模型、理论、算法和应用。半参数方法特别适用于此类数据，因为通常对这些数据的结构知之甚少，同时为了避免“维度诅咒”，必须进行降维步骤。因此，本项目的主要重点是通过拟合单一指数或多重指数模型，或通过截断扩展的功能数据中包含的术语数，以预测的形式减少维数。这个项目的另一个重点是统计方法，它考虑到曲线数据通常是随机曲线，受单独变化的时间尺度的影响。这导致了函数数据时间扭曲的模型、理论、方法和算法。在基因表达谱传播最受关注的遗传学领域，以及在衰老和死亡率领域，曲线数据非常丰富。研究者将开发功能回归、相关、判别和聚类分析的方法。这些方法将提供工具来建立随机函数之间的关系，并允许将观察到的样本曲线分类为不同的类别。在科学和其他实验和观察研究中收集的大量和日益复杂的数据往往可以被视为曲线或函数。这些数据通常包含有关物理和生物现象的时间动力学的宝贵信息，需要先进的统计技术来提取这些信息。例如，基因微阵列记录的重复cDNA表达数据可能包含有关基因激活模式和基因调控动态的有价值信息。这些数据发挥重要作用的其他例子涉及生殖与衰老之间的关系，衰老与长寿的动态结构，或连续记录的各种血液蛋白之间的关系。研究者将开发专门用于分析和解释这些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.