Collaborative Research: A Symphony of Smoothing and Change Point Analysis

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A sudden change in a real life process is often of particular interest since the change may signal an anomaly, the onset of a disease, or an out-of-control process. What has been ignored in the literature is the co-existence of a slowly-changing component that also needs to be properly modeled to make valid statistical inference. In traditional statistics, inferring a sudden change and modeling a slowly-changing trend are often perceived as two seemingly conflicting concepts since they emphasize respectively on continuity and discontinuity of the true underlying process. Motivated by real-life applications, this project aims to develop three sets of novel statistical methods where simultaneous modeling of the sudden change and the slowly-changing trend are properly introduced to accommodate the practical needs. The statistical analysis tools developed in this project will benefit practitioners in the fields of cybersecurity, environmental sciences, financial managements, and medical studies. The results from the project will be integrated into teaching and student training, and be disseminated through publications and the distribution of R packages.This project aims to the development of statistical methods that are natural fusions of change point analysis and nonparametric smoothing. The proposed method will combine recent developments in functional data analysis and nonparametric smoothing inference, such as functional time series and functional Bahadur representation, and change point analysis tools to solve the challenging problems. The first aim of the project focuses on change point detection in variance functions along with a smoothly-changing mean trend. A novel subsampling approach will be designed to incorporate the large sample size involved. The other two aims of the project are to develop change point detection methods and derive corresponding optimal theoretical properties for multivariate probability densities and functional time series, respectively.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.