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Statistical Inference for High-Dimensional Time Series

高维时间序列的统计推断

基本信息

批准号：
1807023
负责人：
Xiaofeng Shao
金额：
$ 12万
依托单位：
University of Illinois at Urbana-Champaign
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-08-15 至 2022-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1807023&HistoricalAwards=false
关键词：
Statistical Inference Dimensional Time Series

项目摘要

Due to the rapid development of information technologies and their applications in many scientific fields, high dimensional time series (HDTS) are routinely collected nowadays. The methods and theory developed for the inference of low and fixed dimensional time series may not be applicable when the dimension is comparable to or exceeds time series length, and there is an urgent need to develop new statistical methods that can accommodate both high dimensionality and temporal dependence. Statistical inference for HDTS is fundamentally important and has many applications in disciplines ranging from climate science to medical imaging and finance, among others.This project aims to develop innovative theory and methodologies to address several important inference problems in the analysis of HDTS. The research is built on the self-normalized approach, which has found great success in dealing with low dimensional problems. Its advance to the high dimensional context is challenging both methodologically and theoretically, and it requires a new methodological formulation and new theory. This project covers the inference of the mean, covariance matrix, and auto-covariance matrix for HDTS, and the tests developed can be used to detect change points, certain structure of the covariance matrix and target dense alternative. On the theoretical front, the weak convergence of sequential U-statistic based process will be investigated and is of independent interest.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

随着信息技术的迅速发展及其在各个科学领域的应用，高维时间序列（HDTS）已成为一种常规的数据采集方式。当维数与时间序列长度相当或超过时间序列长度时，为推断低维和固定维时间序列而开发的方法和理论可能不适用，并且迫切需要开发新的统计方法，该方法可以容纳高维和时间依赖性。HDTS的统计推断非常重要，在气候科学、医学成像和金融等学科中有许多应用。本项目旨在发展创新的理论和方法，以解决HDTS分析中的几个重要推断问题。研究是建立在自规范化的方法，这已经发现在处理低维问题取得了巨大的成功。它向高维语境的推进在方法论和理论上都具有挑战性，需要新的方法论表述和新的理论。该项目涵盖了HDTS的平均值，协方差矩阵和自协方差矩阵的推断，并且开发的测试可用于检测变点，协方差矩阵的某些结构和目标密集替代。在理论方面，将研究基于顺序U统计的过程的弱收敛，这是独立的兴趣。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。