Martingale Methods in Statistics - Yoichi Nishiyama

Martingale Methods in Statistics

Buch | Hardcover
260 Seiten
2021
Crc Press Inc (Verlag)
978-1-4665-8281-1 (ISBN)
129,95 inkl. MwSt
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 provides a unique introduction to statistics of stochastic processes written with the author’s strong desire to present what is not available in other textbooks. While the author chooses to omit the well-known proofs of some of fundamental theorems in martingale theory by making clear citations instead, the author does his best to describe some intuitive interpretations or concrete usages of such theorems. On the other hand, the exposition of relatively new theorems in asymptotic statistics is presented in a completely self-contained way. Some simple, easy-to-understand proofs of martingale central limit theorems are included.

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.

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.

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.

Erscheint lt. Verlag 10.12.2021
Reihe/Serie Chapman & Hall/CRC Monographs on Statistics and Applied Probability
Zusatzinfo 9 Line drawings, black and white; 9 Illustrations, black and white
Verlagsort Bosa Roca
Sprache englisch
Maße 156 x 234 mm
Gewicht 453 g
Themenwelt Mathematik / Informatik Mathematik Statistik
ISBN-10 1-4665-8281-2 / 1466582812
ISBN-13 978-1-4665-8281-1 / 9781466582811
Zustand Neuware
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