Representative Points of Statistical Distributions

Applications in Statistical Inference
1. Auflage 2025
ISBN: 978-1-032-96411-9
Verlag: Taylor & Francis Ltd

Buch, Englisch, 352 Seiten, Format (B × H): 178 mm x 254 mm

Statistical simulation has become a cornerstone in statistical research and applications. The aim of the book is to present a comprehensive exploration of various methods for statistical simulation and resampling, focusing on consistency and efficiency. It covers a range of representative points (RPs) – Monte Carlo (MC) RPs, Quasi-Monte Carlo (QMC) RPs, and Mean Square Error (MSE) RPs – and their applications, and includes a collection of recent developments in the field. It also explores other types of representative points, and the corresponding approximate distributions, and delves into the realm of statistical simulation, by exploring the limitations of traditional Monte Carlo methods and the innovations brought about by the bootstrap method. It also introduces other kinds of representative points and the corresponding approximate distributions, such as quasi-Monte Carlo and mean square error methods.

Features:

- Comprehensive exploration of statistical simulation methods: It provides a deep dive into MC methods, Bootstrap methods, and introduces other kinds of representative points and the corresponding approximate distributions, such as quasi-Monte Carlo and mean square error methods.

- Emphasis on consistency and efficiency: It highlights the advantages of these methods in terms of consistency and efficiency, addressing the slow convergence rate of classical statistical simulation.

- Collection of recent developments: It brings together the latest advancements in the field of statistical simulation, keeping readers up-to-date with the most current research.

- Practical applications: The book includes numerous practical applications of various types of representative points (MC-RPs, QMC-RPs, and MSE-RPs) in statistical inference and simulation.

- Educational resource: It can serve as a textbook for postgraduate students, a reference book for undergraduate students, and a valuable resource for professionals in various fields.

The book serves as a valuable resource for postgraduate students, researchers, and practitioners in statistics, mathematics, and other quantitative fields.

Zielgruppe

Academic and Postgraduate

Autoren/Hrsg.

Ye, Huajun

Fang, Kai-Tai

Zhou, Yongdao

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

1. Statistical Distributions and Preliminary. 2. Approximated Discretization Methods to A Given Continuous Distribution. 3. Property and Generation of MSE-RPs of Univariate Distributions. 4. Statistical Simulation via Distributions formed by RPs. 5. Estimation of MSE-RPs and Resampling. 6. RPs of Multivariate Distributions. 7. Properties of MSE-RPs of Multivariate Distributions. 8. Applications of RPs in Various Fields. 9. Representative Points for Discrete Massive Data.

Über Autor(innen)

Kai-Tai Fang is a reputable statistician. He was educated at Peking University and The
Chinese Academy of Sciences for undergraduate and postgraduate studies. He was elected
as a Fellow by the Institute of Mathematical Statistics (IMS) in 1992 and a Fellow by
the American Statistical Association (ASA) in 2001 as well as an elective member of the
International Statistical Institute (ISI) in 1985. Professor Fang visited Yale University and
Stanford University for two years and was invited as a Guest Professor at the Swiss Federal
Institute of Technology and a Visiting Professor at the University of North Carolina at
Chapel Hill. He was Chair Professor of the Department of Mathematics at Hong Kong
Baptist University from 1993 to January 2006. Now, he is a Chair Professor at BNUHKBU
United International College. His research interests are in statistics and mathematics,
specifically experimental design, multivariate analysis, and data mining. He published 24
books (including six monographs in English) and more than 300 referred papers.

Huajun Ye received a Bachelor and a Master’s degrees in Probability and Mathematical
Statistics from Peking University in 1999 and 2002, respectively. He received a PhD
in Statistics from Manchester University, U.K. 2005, and his PhD research on covariance
structures modeling of longitudinal data. In 2007, He joined BNU-HKBU United International
College as an Assistant Professor. Now, he is a full Professor in the Department
of Statistics and Data Science at BNU-HKBU United International College. His research
interests include statistical modeling, inference, financial risk management, and statistical
representative points. More than ten research papers have been published in international
journals and conferences, including Biometrika, Mathematics, Journal of Complexity, Journal
of Statistical Computation and Simulation, etc.

Yongdao Zhou received a B.S. degree in pure mathematics in 2002 and M.S. and Ph.D.
in Statistics in 2005 and 2008, respectively, from Sichuan University, China. He was a postdoctoral
fellow at HKBU-UIC Joint Institute of Research Studies. Then, he joined Sichuan
University and was a full professor after 2015. In 2017, he joined Nankai University, where
he is presently a full professor in statistics. He visited UCLA, the University of Manchester,
the National University of Singapore, and Simon Fraser University as a visiting scholar.
His research agenda focuses on experimental design and big data analysis. He published
over 70 papers, such as in JRSSB, JASA, Biometrika, and IEEE TKDE, as well as eight
monographs and textbooks. His research publications have won two best paper awards.