統計数学セミナー

過去の記録 ~02/02次回の予定今後の予定 02/03~

担当者 吉田朋広、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.

2022年02月16日(水)

14:30-16:00   数理科学研究科棟(駒場) 号室
Zoomでの開催となります。参加希望の方はGoogle Formより前日までにご登録ください。
Teppei Ogihara 氏 (University of Tokyo)
Efficient estimation for ergodic jump-diffusion processes
[ 講演概要 ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home

We study the estimation problem of the parametric model for ergodic jump-diffusion processes. Shimizu and Yoshida (Stat. Inference Stoch. Process. 2006) proposed a quasi-maximum-likelihood estimator based on a thresholding likelihood function that detects the existence of jumps.
In this talk, we consider the efficiency of estimators by using local asymptotic normality (LAN). To show the LAN property, we need to specify the asymptotic behavior of log-likelihood ratios, which is complicated for the jump-diffusion model because the transition probability for no jump is quite different from that for the presence of jumps. We develop techniques to show the LAN property based on transition density approximation. By applying these techniques to the thresholding likelihood function, we obtain the LAN property for the jump-diffusion model. Moreover, we have the asymptotic efficiency of
the quasi-maximum-likelihood estimator in Shimizu and Yoshida (2006) and a Bayes-type estimator proposed in Ogihara and Yoshida (Stat.Inference Stoch. Process. 2011). This is a joint work with Yuma Uehara (Kansai University).
[ 参考URL ]
https://docs.google.com/forms/d/e/1FAIpQLSeRTEo19DJgFiVsEpLrRapqzkL6LZAiUMGdA0ezK-nWYSPrGg/viewform