Change Point Analysis

A crucial statistical technique for detecting structural breaks within datasets, applicable in diverse fields such as finance and weather forecasting.

Change point analysis is a crucial statistical technique for detecting structural breaks within datasets, applicable in diverse fields such as finance and weather forecasting. The authors of this book aim to consolidate recent advancements and broaden the scope beyond traditional time series applications to include biostatistics, longitudinal data analysis, high-dimensional data, and network analysis.

The book introduces foundational concepts with practical data examples from literature, alongside discussions of related machine learning topics. Subsequent chapters focus on mathematical tools for single- and multiple-change point detection along with statistical inference issues, which provide rigorous proofs to enhance understanding but assume readers have foundational knowledge in graduate-level probability and statistics. The book also expands the discussion into threshold regression frameworks linked to subgroup identification in modern statistical learning and apply change point analysis to functional data and dynamic networks-areas not comprehensively covered elsewhere.

Key Features:

• Comprehensive Coverage of Diverse Applications: This book expands the scope of change point analysis to include biostatistics, longitudinal data, high-dimensional data, and network analysis. This broad applicability makes it a valuable resource for researchers and students across various disciplines
• Integration of Theory and Practice: The book balances rigorous mathematical theory with practical applications by providing extensive computational examples using R. Each chapter features real-world data illustrations and discussions of relevant machine learning topics, ensuring that readers can see the relevance of theoretical concepts in applied settings

• Accessibility for Students: The content is designed with graduate-level students in mind, providing clear explanations and structured guidance through complex mathematical tools. Rigorous proofs are included to facilitate understanding without overwhelming readers with overly advanced theories early on The book incorporates computational results using R, showcasing various packages tailored for specific methods or problem domains while providing references for further exploration. By offering a selection of widely adopted methodologies relevant in scientific research as well as business contexts, this text aims to equip junior researchers with essential tools needed for their work in change point analysis.

  Autorentext

  Baisuo Jin is a professor at University of Science and Technology of China. His research fields include spatial statistics, random matrix and change point. His research works have been accepted for publication in premium journals including The Proceedings of the National Academy of Sciences (PNAS), The Annals of Statistics, and Biometrika.

Jialiang Li is a professor at Department of Statistics and Data Science, National University of Singapore. He was elected as Elected Member of International Statistical Institute (ISI) in 2019, Fellow of American Statistical Association (ASA) in 2020 and Fellow of Institute of Mathematical Statistics (IMS) in 2022. He has served on the editorial board for Annals of Applied Statistics, Annual Review of Statistics and Its Application, Biometrics, Biostatistics & Epidemiology, Lifetime Data Analysis and Statistical Methods in Medical Research.

Inhalt

1. Overview. 2. Single change point. 3. Multiple change points. 4. Interval estimation. 5. Regression models with change points. 6. Further Applications.