Collaborative Research: Spectral Functional Principal Components on Abelian Groups with Applications to Spatial Functional Data

合作研究：阿贝尔群的谱函数主成分及其在空间函数数据中的应用

• 批准号: 1914882
• 负责人: Piotr Kokoszka
• 金额: $ 12.01万
• 依托单位: Colorado State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-08-01 至 2023-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1914882&HistoricalAwards=false
• 关键词: Collaborative; Research; Spectral; Functional; Principal

Massive data sets on gridded 2D and 3D domains have recently become available through computer climate model outputs, records from satellite remote sensing and brain scans, among others. These data sets have both temporal and spatial dimension. For example, a state of vegetation is observed on a grid covering an agricultural area at regular time intervals, every day or every week. Such data can be viewed as functions of time, one function per spatial grid unit. Their chief characteristic is the spatial dependence of curves observed at the grid nodes. There is an increasing need to develop statistical tools, which will allow researchers to extract useful information from such data. The PIs will develop such tools. The data and problems that motivate this research arise in several science fields, which have important impacts on society. For example, conclusions drawn from future climate models help the government and corporations plan for the allocation of various assets. Brain research on trauma experienced by military veterans and on Alzheimer's disease are recognized as important societal goals. The statistical research the PIs will conduct will provide useful quantitative tools to help scientists in these fields. Mathematical foundations of the new approach will be created, together with domain-specific approaches. The new methods will be implemented in R packages and made available to research community, government agencies and commercial enterprises. In the course of the proposed research, two Ph.D. students will be trained. The PIs will create a new framework for inference for functional data defined on domains with an additive group structure. The new dimension reduction approach will have characteristics of a multi-scale, data-driven representation, which takes into account the dependence of the functions defined on group elements, for example spatial grid nodes. The PIs will use methods of Fourier analysis on Abelian groups, spectral theory for functional data, invariance principles in Hilbert spaces, computationally efficient spatio-temporal spline representations, routines for downloading and manipulating massive data sets. The PIs will develop several inferential procedures, including bootstrap-based inference, tests for the spatial and distributional structure, and applications to the evaluation of the accuracy of computer climate models. The PIs will also develop corresponding computational techniques, which will lead to the computationally fast representation of various data structures of large to massive size.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.

最近，通过计算机气候模型输出、卫星遥感记录和大脑扫描等方式，可以获得网格2D和3D领域的海量数据集。这些数据集既有时间维度，也有空间维度。例如，在覆盖农业区的网格上以固定的时间间隔、每天或每周观察植被的状态。这样的数据可以被视为时间的函数，每个空间网格单元一个函数。它们的主要特征是在网格节点处观察到的曲线的空间相关性。人们越来越需要开发统计工具，使研究人员能够从这些数据中提取有用的信息。私人投资公司将开发这样的工具。推动这项研究的数据和问题出现在几个对社会有重要影响的科学领域。例如，从未来气候模型得出的结论有助于政府和企业规划各种资产的配置。对退伍军人经历的创伤和阿尔茨海默病的脑研究被认为是重要的社会目标。私人投资研究所将进行的统计研究将提供有用的量化工具，帮助这些领域的科学家。将创建新方法的数学基础，以及特定领域的方法。新方法将在R包中实施，并向研究社区、政府机构和商业企业提供。在拟议的研究过程中，将培训两名博士生。PI将为在具有附加基团结构的域上定义的功能数据创建一个新的推理框架。新的降维方法将具有多尺度、数据驱动的表示法的特点，它考虑到定义的函数对组元素的依赖，例如空间网格节点。PI将使用关于阿贝尔群的傅立叶分析方法、函数数据的谱理论、希尔伯特空间中的不变性原理、计算高效的时空样条表示法、用于下载和处理海量数据集的例程。PIS将开发几个推理程序，包括基于自举的推理、空间和分布结构的测试，以及应用于评估计算机气候模型的准确性。PIS还将开发相应的计算技术，这将导致从大型到大规模的各种数据结构的计算快速表示。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Frequency domain theory for functional time series: Variance decomposition and an invariance principle

函数时间序列的频域理论：方差分解和不变性原理

• DOI: 10.3150/20-bej1199
• 发表时间: 2020
• 期刊: Bernoulli
• 影响因子: 1.5
• 作者: Kokoszka, Piotr;Mohammadi Jouzdani, Neda
• 通讯作者: Mohammadi Jouzdani, Neda

MONITORING FOR A CHANGE POINT IN A SEQUENCE OF DISTRIBUTIONS

• DOI: 10.1214/20-aos2036
• 发表时间: 2021-08-01
• 期刊: ANNALS OF STATISTICS
• 影响因子: 4.5
• 作者: Horvath, Lajos;Kokoszka, Piotr;Wang, Shixuan
• 通讯作者: Wang, Shixuan

Renewal model for anomalous traffic in Internet2 links

Internet2链路异常流量的更新模型

• DOI: 10.1177/1471082x19983146
• 发表时间: 2021
• 期刊: Statistical Modelling
• 影响因子: 1
• 作者: Nicholson, John;Kokoszka, Piotr;Lund, Robert;Kiessler, Peter;Sharp, Julia
• 通讯作者: Sharp, Julia

Principal Component Analysis of Spatially Indexed Functions

• DOI: 10.1080/01621459.2020.1732395
• 发表时间: 2020-03-30
• 期刊: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• 影响因子: 3.7
• 作者: Kuenzer, Thomas;Hormann, Siegfried;Kokoszka, Piotr
• 通讯作者: Kokoszka, Piotr

Quantifying the risk of heat waves using extreme value theory and spatio-temporal functional data

• DOI: 10.1016/j.csda.2018.07.004
• 发表时间: 2019-03
• 期刊: Comput. Stat. Data Anal.
• 作者: J. French;P. Kokoszka;Stilian A. Stoev;Lauren Hall