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Inference for Dynamic Objects

动态对象的推理

基本信息

批准号：
1713108
负责人：
Wolfgang Polonik
金额：
$ 12.5万
依托单位：
University of California-Davis
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-08-01 至 2021-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1713108&HistoricalAwards=false
关键词：
Inference Dynamic Objects

项目摘要

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.

现代数据收集技术产生了源源不断的复杂数据。统计领域有义务为其分析开发工具，使用户能够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。该项目将不仅通过构建相关的新方法，而且通过分析这些方法来应对这些挑战，以便彻底了解它们的优点和缺点。反过来，这将有助于对实际数据分析结果进行诚实的评估和解释。本项目中考虑的复杂数据类型的一个实例是网络数据。一个相关的真实例子是世界贸易网络，它由成对国家之间的贸易指数组成。国家可以分成贸易区块，这个项目将制定方法，以便分析贸易区块之间的依赖结构。这将有助于确定驱动这种依赖的因素，以及它们如何随着时间的推移而变化。更广泛地说，该项目的成果预计将对统计领域和各种应用领域产生影响。为实现这一目标，将通过在国际统计期刊上发表出版物、在国家和国际会议上作介绍以及开发可供社区使用的相关软件/代码，广泛传播在本项目中形成的统计见解、方法和理论。此外，该项目将直接促进现代统计领域的研究生和本科生的培训。预计该项目与加州大学戴维斯分校正在进行的国家科学基金统计研究培训补助金之间将会互惠互利并产生协同效应。该项目寻求开发新的统计方法来分析动态对象数据，特别是网络和功能数据。更具体地说，这个项目将(I)研究随机网络的分层时变区块模型中的相关性结构，并将由此产生的方法应用于经济网络数据的分析，例如贸易网络；(Ii)开发一类随机网络的连续时间点过程模型，允许对这些模型中相应的最大似然估计器进行灵活的模型和分析；(Iii)开发基于经验似然的函数时间序列推理方法。该项目旨在开发一种方法，一方面足够灵活和在计算上可行，对复杂的现实世界应用程序有用，另一方面导致方法允许进行严格的统计分析，从而洞察和理解他们的行为。