Advancing Nonparametric Online Inference: Optimal Uncertainty Quantification and Decision-Making for Streaming Data

This research project will enhance data science by developing new methodologies for uncertainty quantification and decision-making in large-scale, streaming data with complex structures. These novel statistical tools will improve real-time analysis in fields such as mobile health, infectious disease surveillance, and neuroscience. In healthcare, the developed methods will advance diagnostic accuracy and treatment precision across various medical conditions like diabetes and Alzheimer's disease, enabling timely interventions and personalized care strategies based on real-time data analysis.

Additionally, the project will integrate its research into K-12 educational programs and offer training opportunities for graduate and undergraduate students, focusing on engaging underrepresented groups in STEM. This initiative aims to cultivate the next generation of data scientists and statisticians, equipping them with the vital skills needed to address future challenges in data-driven fields.

The research will establish a unified framework for nonparametric online statistical inference using an online multiplier bootstrap approach combined with functional stochastic gradient descent (SGD) algorithms. This framework will include local and global confidence intervals and bands, pattern and signal detection via hypothesis testing, and real-time decision-making strategies for nonparametric regressions.

These methods will be applicable to various data scenarios, from independent to dependent data. The project will characterize the non-asymptotic behavior of the functional SGD estimator, validate the consistency of the multiplier bootstrap method, establish honest confidence bands, and demonstrate minimax optimal testing consistency of the proposed inference tools.

By developing a solid foundation with accompanying software for nonparametric online inference, this research will advance methodologies in online data-driven decision-making, with broad applications ranging from mobile health to financial markets.

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.