Nonparametric Total Variation Regression for Multivariate Process Data

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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.