統計数学セミナー
Seminar on Probability and Statistics |
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Seminar on Probability and Statistics Monday September 25 2006 Tokyo 128 1:00-2:10 pm
Nonparametric testing time-homogeneity for L'evy processes
西山 陽一 / NISHIYAMA, Yoichi 統計数理研究所 / The Institute of Statistical Mathematics 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.
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