Martingale Methods in Statistics: Chapman & Hall/CRC Monographs on Statistics and Applied Probability
Autor Yoichi Nishiyamaen Limba Engleză Paperback – 27 mai 2024
The potential readers include those who hope to build up mathematical bases to deal with high-frequency data in mathematical finance and those who hope to learn the theoretical background for Cox’s regression model in survival analysis. A highlight of the monograph is Chapters 8-10 dealing with Z-estimators and related topics, such as the asymptotic representation of Z-estimators, the theory of asymptotically optimal inference based on the LAN concept and the unified approach to the change point problems via "Z-process method". Some new inequalities for maxima of finitely many martingales are presented in the Appendix. Readers will find many tips for solving concrete problems in modern statistics of stochastic processes as well as in more fundamental models such as i.i.d. and Markov chain models.
Toate formatele și edițiile | Preț | Express |
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Paperback (1) | 316.92 lei 6-8 săpt. | |
CRC Press – 27 mai 2024 | 316.92 lei 6-8 săpt. | |
Hardback (1) | 766.61 lei 6-8 săpt. | |
CRC Press – 24 noi 2021 | 766.61 lei 6-8 săpt. |
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Specificații
ISBN-13: 9781032146041
ISBN-10: 1032146044
Pagini: 260
Ilustrații: 18
Dimensiuni: 156 x 234 mm
Greutate: 0.4 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Chapman & Hall/CRC Monographs on Statistics and Applied Probability
Locul publicării:Boca Raton, United States
ISBN-10: 1032146044
Pagini: 260
Ilustrații: 18
Dimensiuni: 156 x 234 mm
Greutate: 0.4 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Chapman & Hall/CRC Monographs on Statistics and Applied Probability
Locul publicării:Boca Raton, United States
Cuprins
1. Prologue 2 Preliminaries. 3. A Short Introduction to Statistics of Stochastic Processes. 4. Discrete-Time Martingales. 5. Continuous-Time Martingales. 6. Tools of Semimartingales. 7. Tools for Asymptotic Statistics. 8. Parametric Z-Estimators. 9. Optimal Inference in Finite-Dimensional LAN Models. 10 Z-Process Method for Change Point Problems.
Notă biografică
Yoichi Nishiyama is a professor in mathematical statistics and probability at the School of International Liberal Studies of Waseda University; he is also engaged in the education of master’s and doctoral students at the Department of Pure and Applied Mathematics at the same university. Prior to his assignment to Waseda University, he worked at the Institute of Statistical Mathematics, Tokyo, from 1994 to 2015. He was the Editor-in-Chief of Journal of the Japan Statistical Society and a Co-Editor of Annals of the Institute of Statistical Mathematics and he received the JSS Ogawa Award from the Japan Statistical Society in 2009.
Recenzii
"This book is expected to be an excellent reference for researchers who need to perform statistical analysis based on the martingale theory. It is very rare to find a book that systematically and rigorously summarizes martingale theory from the point of view of its application to statistics. This textbook harmonically organizes the mathematical facts related to martingales and their statistical applications, and by doing so, it helps researchers to establish a theoretically concrete foundation. Therefore, this book can be evaluated as an excellent textbook where mathematics and statistics meet together."
-Insuk Seo, in Journal of the American Statistical Association, November 2023
"The martingale theory is an important topic in probability theory and related tools have been widely applied in statistical analysis, such as financial data or survival analysis. ...This book well summarizes useful tools in martingale and provides rigorous theorems. ... In summary, this book is a nice reference because of rich and comprehensive materials in martingale
theory. This book is suitable to researchers who are working on related research topics."
- Li-Pang Chen, in Journal of the Royal Statistical Society: Series A, April 2022
-Insuk Seo, in Journal of the American Statistical Association, November 2023
"The martingale theory is an important topic in probability theory and related tools have been widely applied in statistical analysis, such as financial data or survival analysis. ...This book well summarizes useful tools in martingale and provides rigorous theorems. ... In summary, this book is a nice reference because of rich and comprehensive materials in martingale
theory. This book is suitable to researchers who are working on related research topics."
- Li-Pang Chen, in Journal of the Royal Statistical Society: Series A, April 2022
Descriere
This gives a comprehensive introduction to the (standard) statistical analysis based on the theory of martingales and develops entropy methods in order to treat dependent data in the framework of martingales. The author starts a summary of the martingale theory, and then proceeds to give full proofs of the martingale central limit theorems.