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Seminar on Probability and Statistics
Seminar information archive ～04/26｜Next seminar｜Future seminars 04/27～
| Organizer(s) | Nakahiro Yoshida, Teppei Ogihara, Yuta Koike |
|---|
2020/04/16
17:00-18:10 Room #φ (Graduate School of Math. Sci. Bldg.)
Masatoshi Goda (University of Tokyo)
Hawkes process and Edgeworth expansion with application to Maximum Likelihood Estimator (JAPANESE)
https://docs.google.com/forms/d/18MDagC71CtB7SJmW2s0tPIBW9YDUNWH5XH1uby2W6Xc/edit
Masatoshi Goda (University of Tokyo)
Hawkes process and Edgeworth expansion with application to Maximum Likelihood Estimator (JAPANESE)
[ Abstract ]
The Hawkes process is a point process with a self-exciting property. It has been used to model earthquakes, social media events, infections, etc. and is getting a lot of attention. However, as a real problem, there are often situations where we can not obtain data with sufficient observation time. In such cases, it is not appropriate to approximate the error distribution of an estimator by the normal distribution. We established the Edgeworth expansion for a functional of a geometric mixing process, and applied this scheme to a functional of the Hawkes process with an exponential kernel. Furthermore, we gave a more appropriate asymptotic distribution for the error of the Maximum Likelihood Estimator of the Hawks process, i.e. a higher-order asymptotic distribution than the normal distribution. Here, in addition to the details of these statements, we also present the simulation results.
[ Reference URL ]The Hawkes process is a point process with a self-exciting property. It has been used to model earthquakes, social media events, infections, etc. and is getting a lot of attention. However, as a real problem, there are often situations where we can not obtain data with sufficient observation time. In such cases, it is not appropriate to approximate the error distribution of an estimator by the normal distribution. We established the Edgeworth expansion for a functional of a geometric mixing process, and applied this scheme to a functional of the Hawkes process with an exponential kernel. Furthermore, we gave a more appropriate asymptotic distribution for the error of the Maximum Likelihood Estimator of the Hawks process, i.e. a higher-order asymptotic distribution than the normal distribution. Here, in addition to the details of these statements, we also present the simulation results.
https://docs.google.com/forms/d/18MDagC71CtB7SJmW2s0tPIBW9YDUNWH5XH1uby2W6Xc/edit
