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Seminar on Probability and Statistics
Seminar information archive ～04/25｜Next seminar｜Future seminars 04/26～
| Organizer(s) | Nakahiro Yoshida, Teppei Ogihara, Yuta Koike |
|---|
2006/09/25
13:00-14:10 Room #128 (Graduate School of Math. Sci. Bldg.)
西山 陽一 (統計数理研究所)
Nonparametric testing time-homogeneity for L'evy processes
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/09.html
西山 陽一 (統計数理研究所)
Nonparametric testing time-homogeneity for L'evy processes
[ Abstract ]
First, a review about uniform central limit theorems for martingales is given. The main part of the talk is concerned with a change point problem for L'evy processes. The null hypothesis is that the L'evy process is time-homogeneous, and the alternative is that the L'evy measure changes at a certain time point of the observation period. We propose an empirical process type statistics, and derive its asymptotic behaviour under the null and the alternative hypotheses. The limiting distribution under the null hypothesis is a functional of the standard Brownian motion.
[ Reference URL ]First, a review about uniform central limit theorems for martingales is given. The main part of the talk is concerned with a change point problem for L'evy processes. The null hypothesis is that the L'evy process is time-homogeneous, and the alternative is that the L'evy measure changes at a certain time point of the observation period. We propose an empirical process type statistics, and derive its asymptotic behaviour under the null and the alternative hypotheses. The limiting distribution under the null hypothesis is a functional of the standard Brownian motion.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/09.html
