Nonparametric Total Variation Regression for Multivariate Process Data

多元过程数据的非参数总变差回归

基本信息

批准号：
2210929
负责人：
Michael Pokojovy
金额：
$ 11.99万
依托单位：
University of Texas at El Paso
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-09-15 至 2023-12-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2210929&HistoricalAwards=false
关键词：
Nonparametric Total Variation Regression Multivariate

项目摘要

Process data of interest frequently occur in engineering, manufacturing, commerce, environmental science and other arenas. For example, water or air contamination levels, configuration of a drilled metal part, chemical composition of a pharmaceutical product, and operational characteristics of computer network, all changing over time, are routinely monitored in real time. Upsets or shifts away from a stable, consistent flow of process data are indicative of special cause intrusion(s). These special causes can be significantly detrimental to decision making and process understanding in the context of a particular application. Development of reference-free statistical control charts for monitoring multivariate processes for both gradual and abrupt changes in the mean vector has been significantly hampered by a lack of suitable nonparametric regression methodology. In response to this challenge, this project will address the acute need for nonparametric estimators for multivariate process data and will develop new reference-free methods for statistical process monitoring. The outcomes of this project will benefit society through enhanced statistical quality assurance in industrial manufacturing, business, commerce, healthcare, and other domains of societal importance. The results of this project will be implemented in a form of publicly available software. Furthermore, the project will involve multiple research training and career mentoring initiatives at various educational levels and will offer multiple opportunities for interdisciplinary training, with a particular focus on broadening participation in statistical sciences.The project will advance the frontiers of nonparametric multivariate regression by developing new theory and methodology of statistical process control for individuals multivariate process data. In the context of nonparametric estimation for independent sub-Gaussian processes, the goal is to investigate nonparametric total variation (TV) and taut string (TS) estimators for multivariate process data with piecewise smooth process mean, establish well-posedness for associated optimization problems, prove their equivalence, and investigate asymptotic consistency/convergence rates for TV/TS estimators in various practically relevant topologies. These theoretical results will be applied to develop computationally efficient algorithmic implementations of the TV/TS estimator, investigate convergence and complexity of these algorithms, and showcase their performance based on synthetic and real data. Subsequently, algorithmic implementations of the TV/TS estimator will be used to design a new class of reference-free statistical control charts for nonparametric monitoring of multivariate process mean and compare them to state-of-the-art competitors under a variety of practically relevant scenarios.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.

感兴趣的过程数据经常发生在工程，制造，商业，环境科学和其他领域。例如，经常对水或空气污染水平，钻孔金属部分的配置，药品的化学成分以及计算机网络的运行特征，所有这些都会随着时间的推移而变化。兴奋或偏离稳定，一致的过程数据流的转移表明特殊原因入侵。这些特殊原因可能对在特定应用程序的背景下对决策和处理理解有很大损害。由于缺乏合适的非参数回归方法，开发用于监测平均矢量逐渐变化和突然变化的多元过程的无参考统计控制图。为了应对这一挑战，该项目将解决多元过程数据非参数估计器的急需需求，并将开发用于统计过程监视的新的无参考方法。该项目的结果将通过提高工业制造，商业，商业，医疗保健和其他社会重要性领域的统计质量保证来使社会受益。该项目的结果将以公开可用的软件形式实施。此外，该项目将在各种教育水平上涉及多个研究培训和职业指导计划，并为跨学科培训提供多个机会，特别着重于扩大参与统计科学的参与。该项目将通过开发新的统计过程和跨越统计过程的方法来促进非参数多元学院回归的领域。 In the context of nonparametric estimation for independent sub-Gaussian processes, the goal is to investigate nonparametric total variation (TV) and taut string (TS) estimators for multivariate process data with piecewise smooth process mean, establish well-posedness for associated optimization problems, prove their equivalence, and investigate asymptotic consistency/convergence rates for TV/TS estimators in various practically relevant topologies.这些理论结果将用于开发电视/TS估计器的计算有效算法实现，研究这些算法的收敛性和复杂性，并根据合成和真实数据来展示其性能。 Subsequently, algorithmic implementations of the TV/TS estimator will be used to design a new class of reference-free statistical control charts for nonparametric monitoring of multivariate process mean and compare them to state-of-the-art competitors under a variety of practically relevant scenarios.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 标准。