Martingale Methods in Statistics

ISBN-13: 9781466582811 / Angielski / Twarda / 2021 / 246 str.

Yoichi Nishiyama

Opis

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. In addition, the book presents some general theories for semiparametric Z-estimation and semiparametric change point problem, with new examples.

Recenzje

"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

Spis treści

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.

O autorze

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.