Theory and Methods for Estimation of Nonsmooth Functionals and Detection of Simultaneous Signals

现在，高维数据的收集和分析在包括基因组学、生物信息学、气候研究和信号处理在内的广泛科学应用中具有核心重要性。这种高维数据的分析面临着许多新的挑战，这一领域迫切需要发展新的统计理论和方法。尽管在许多应用中，高维数据通常使用复杂的模型进行分析，但人们的注意力往往集中在测试低维的特定假设上。在这种情况下，新的统计理论和方法依赖于估计非光滑泛函的新技术的发展，这是本项目的主题。本研究的重点是建立一种全面的估计非光滑泛函的方法，并展示如何将该方法用于基因组学中遇到的多个高维稀疏序列的检测和测试。这项拟议的研究将为科学家提供新的方法来分析这种高度复杂的数据。本项目制定的统计程序将以高级编程语言执行，并与相关研究报告一起在互联网上提供，以便与其他方法进行比较。

The collection and analysis of high dimensional data is now of central importance in a wide range of scientific applications, including genomics, bioinformatics, climate studies, and signal processing. There are many new challenges in the analysis of such high dimensional data and there is much demand for the development of new statistical theory and methodology in this field. Although high dimensional data is often analyzed using complex models in many applications, attention is often focused on testing specific hypotheses that are of low dimension. In such cases new statistical theory and methodology relies on the development of new techniques for estimating non-smooth functionals, the topic of this project.The focus of this research project is to establish a comprehensive methodology for estimating non-smooth functionals and to show how this methodology can be used in the detection and testing of multiple high-dimensional sparse sequences encountered in genomics. The proposed research will provide scientists with new methodologies to analyze such highly complex data. The statistical procedures developed in this project will be implemented in a high-level programming language and made available on the internet with the related research reports so as to allow comparisons with other approaches.