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Martingale Methods in Statistics Yoichi Nishiyama (School of International Liberal Studies, Faculty of International Research and Education, Waseda University)

Martingale Methods in Statistics By Yoichi Nishiyama (School of International Liberal Studies, Faculty of International Research and Education, Waseda University)

Martingale Methods in Statistics by Yoichi Nishiyama (School of International Liberal Studies, Faculty of International Research and Education, Waseda University)

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Summary

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.

Martingale Methods in Statistics Summary

Martingale Methods in Statistics by Yoichi Nishiyama (School of International Liberal Studies, Faculty of International Research and Education, Waseda University)

  • Potential readers include those who wish to build up mathematical bases to deal with high-frequency data in mathematical finance and those who wish to learn the theoretical background for Cox's regression model in survival analysis
  • Intuitive interpretations and concrete usages of fundamental theorems in martingale theory
  • Relatively new theorems in asymptotic statistics presented in a completely self-contained way.
  • Highlight of the monograph is Chapters 8-10 dealing with Z-estimators and related topics

Martingale Methods in Statistics Reviews

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

About Yoichi Nishiyama (School of International Liberal Studies, Faculty of International Research and Education, Waseda University)

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.

Table of Contents

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.

Additional information

NPB9781466582811
9781466582811
1466582812
Martingale Methods in Statistics by Yoichi Nishiyama (School of International Liberal Studies, Faculty of International Research and Education, Waseda University)
Yoichi Nishiyama (School of International Liberal Studies, Faculty of International Research and Education, Waseda University)
Chapman & Hall/CRC Monographs on Statistics and Applied Probability
New
Hardback
Taylor & Francis Inc
2021-11-24
260
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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