## Seminar on Probability and Statistics

Organizer(s) Nakahiro Yoshida, Teppei Ogihara, Yuta Koike

### 2022/02/16

14:30-16:00   Room # (Graduate School of Math. Sci. Bldg.)
Teppei Ogihara (University of Tokyo)
Efficient estimation for ergodic jump-diffusion processes
[ Abstract ]
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).
[ Reference URL ]
https://docs.google.com/forms/d/e/1FAIpQLSeRTEo19DJgFiVsEpLrRapqzkL6LZAiUMGdA0ezK-nWYSPrGg/viewform