統計数学セミナー

過去の記録 ~06/12次回の予定今後の予定 06/13~

担当者 吉田朋広、増田弘毅、荻原哲平、小池祐太
セミナーURL http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/
目的 確率統計学およびその関連領域に関する研究発表, 研究紹介を行う.

2021年02月17日(水)

14:30-15:30   数理科学研究科棟(駒場) Zoom号室
参考URLのGoogle Formより3日前までに参加登録してください。 ご登録後、会議参加に必要なURLを送付いたします。
Nakahiro Yoshida 氏 (University of Tokyo)
Quasi-likelihood analysis for stochastic differential equations: volatility estimation and global jump filters (ENGLISH)
[ 講演概要 ]
Asia-Pacific Seminar in Probability and Statistics https://sites.google.com/view/apsps/home

The quasi likelihood analysis (QLA) is a framework of statistical inference for stochastic processes, featuring the quasi-likelihood random field and the polynomial type large deviation inequality. The QLA enables us to systematically derive limit theorems and tail probability estimates for the associated QLA estimators (quasi-maximum likelihood estimator and quasi-Bayesian estimator) for various dependent models. The first half of the talk will be devoted to an introduction to the QLA for stochastic differential equations. The second half presents recent developments in a filtering problem to estimate volatility from the data contaminated with jumps. A QLA for volatility for a stochastic differential equation with jumps is constructed, based on a "global jump filter" that uses all the increments of the process to decide whether an increment has jumps.


Key words: stochastic differential equation, high frequency data, Le Cam-Hajek theory, Ibragimov-Has'minskii-Kutoyants program, polynomial type large deviation inequality, quasi-maximum likelihood estimator, quasi-Bayesian estimator, L^p-estimates of the error, non-ergodic statistics, asymptotic (mixed) normality.
[ 参考URL ]
https://docs.google.com/forms/d/e/1FAIpQLSeLrq_Ifc4WvJC6uvwIpMyrAVM9v-0J3FOaZbsplbU9d21ALw/viewform