Inference for Dynamic Objects

现代数据收集技术产生了稳定的复杂数据流。统计领域有义务开发分析工具，让用户得出有意义和正确的结论。鉴于所收集数据的复杂性，这是一项具有挑战性的任务。本项目将解决这些挑战，不仅通过构建相关的新方法，而且通过分析这些方法，以建立对其优缺点的透彻理解。反过来，这将有助于对实际数据分析结果进行诚实的评价和解释。本项目中考虑的复杂数据类型的一个实例是网络数据。一个相关的现实例子是世界贸易网络，它由国家对之间的贸易指数组成。各国可以分成贸易集团，本项目将制定方法，分析贸易集团之间的依赖结构。这将有助于确定驱动这种依赖的因素，以及它们如何随时间变化。更一般地说，这个项目的成果预计将影响统计领域和各个应用领域。为此，将通过在国际统计期刊上的出版物、在国家和国际会议上的发言，广泛传播在这个项目中发展起来的统计见解、方法和理论，并开发向社区提供的有关软件/代码。此外，该项目将直接有助于培养现代统计领域的研究生和本科生。预计该项目将与加州大学戴维斯分校正在进行的美国国家科学基金会统计研究培训补助金之间产生互利和协同效应。该项目旨在开发新的统计方法，用于分析动态对象数据，特别是网络和功能数据。更具体地说，该项目将(i)研究随机网络的分层时变块模型中的依赖结构，并将所得方法应用于分析经济网络数据，如贸易网络；（ii）为随机网络开发一类连续时间点过程模型，允许灵活的模型和分析这些模型中相应的最大似然估计量；（iii）为功能时间序列开发基于经验似然的推理方法。该项目的目的是开发方法，一方面，足够灵活和计算上可行，可用于复杂的现实世界的应用程序，另一方面，产生的方法允许严格的统计分析，提供洞察和理解，他们的行为。

Modern data collection techniques result in a steady stream of complex data. The field of statistics has an obligation to develop tools for their analysis, allowing users to draw meaningful and correct conclusions. In view of the complexity of the collected data, this is a challenging task. This project will tackle these challenges by not only constructing relevant novel methodologies, but by also analyzing these methods in order to establish a thorough understanding of their strengths and weaknesses. This, in turn, will facilitate an honest evaluation and interpretation of practical data analysis results. One instance of a complex data type considered in this project is network data. A relevant real-world example is the world trade network, consisting of trading indices between pairs of countries. Countries can be grouped into trading blocks, and this project will develop methodology allowing the analysis of the dependence structure between the trading blocks. This will help to identify factors that are driving this dependence, and how they change over time. More generally, the outcomes of this project are expected to impact the field of statistics and various fields of application. This will be achieved by widely disseminating statistical insight, methodologies and theory developed in this project through publications in international statistics journals, presentations at national and international conferences, and by developing relevant software/code to be made available to the community. Moreover, this project will directly contribute to the training of both graduate students and undergraduate students in modern fields of statistics. It is expected that there will be mutual benefits and synergies between this project and the ongoing NSF Research Training Grant in Statistics at UC Davis. This project seeks to develop novel statistical methods for the analysis of dynamic object data, in particular, networks and functional data. More specifically, this project will (i) study dependence structures in hierarchical time-varying block models for stochastic networks, and apply the resulting methodologies to the analysis of economic network data such as trade networks; (ii) develop a class of continuous-time point process models for random networks, allowing for a flexible model and analysis of the corresponding maximum likelihood estimators in these models; (iii) develop empirical likelihood based inference methodology for functional time series. The project aims at developing methodologies that, on the one hand, are flexible enough and computationally feasible to be useful for complex real-world applications, and that, on the other hand, result in methodologies that allow rigorous statistical analyses providing insight into, and understanding of, their behavior.