Nonparametric Total Variation Regression for Multivariate Process Data

多元过程数据的非参数总变差回归

• 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

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出现在工程、制造、商业、环境科学和其他领域。例如，水或空气污染水平、钻孔金属部件的配置、药物产品的化学成分以及计算机网络的操作特性（所有这些都随时间变化）都被真实的定期地监测。扰乱或偏离稳定、一致的过程数据流表示特殊原因入侵。 这些特殊原因可能对特定应用环境中的决策制定和过程理解产生重大不利影响。由于缺乏合适的非参数回归方法，开发无参考统计控制图来监测多变量过程中平均向量的渐变和突变一直受到显着阻碍。为了应对这一挑战，该项目将解决多变量过程数据的非参数估计的迫切需要，并将开发新的无参考方法的统计过程监测。该项目的成果将通过加强工业制造，商业，商业，医疗保健和其他具有社会重要性的领域的统计质量保证来造福社会。该项目的成果将以公开软件的形式实施。此外，该项目将涉及多个研究培训和职业指导举措，在不同的教育水平，并将提供多个跨学科的培训机会，特别是侧重于扩大参与统计科学，该项目将推进非参数多元回归的前沿，通过开发新的理论和方法的统计过程控制的个人多元过程数据。在独立的次高斯过程的非参数估计的背景下，我们的目标是调查非参数全变差（TV）和拉紧弦（TS）估计的多变量过程数据与分段光滑过程均值，建立适定性相关的优化问题，证明其等价性，并调查渐近一致性/收敛速度TV/TS估计在各种实际相关的拓扑结构。这些理论结果将被应用于开发计算效率的算法实现的TV/TS估计，调查这些算法的收敛性和复杂性，并展示其性能的基础上合成和真实的数据。随后，委员会注意到，TV/TS估计器的算法实现将用于设计一类新的无参考统计控制图，用于多变量过程均值的非参数监测，并将它们与状态控制图进行比较。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响进行评估，被认为值得支持审查标准。

项目成果

A hybrid method for density power divergence minimization with application to robust univariate location and scale estimation

密度功率散度最小化的混合方法，应用于稳健的单变量位置和尺度估计

• DOI: 10.1080/03610926.2023.2209347
• 发表时间: 2023
• 期刊: Communications in Statistics - Theory and Methods
• 作者: Anum, Andrews T.;Pokojovy, Michael
• 通讯作者: Pokojovy, Michael