Seminar on Probability and Statistics

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

2017/05/18

15:00-16:10   Room #117 (Graduate School of Math. Sci. Bldg.)
Alexander A. Novikov (University of Technology Sydney)
On a representation of fractional Brownian motion and the limit distributions of statistics arising in cusp statistical models
[ Abstract ]
We discuss some extensions of results from the recent paper by Chernoyarov et al. (Ann. Inst. Stat. Math. October 2016) concerning limit distributions of Bayesian and maximum likelihood estimators in the model "signal plus white noise" with irregular cusp-type signals. Using a new representation of fractional Brownian motion (fBm) in terms of cusp functions we show that as the noise intensity tends to zero, the limit distributions are expressed in terms of fBm for the full range of asymmetric cusp-type signals correspondingly with the Hurst parameter H, 0<H<1. Simulation results for the densities and variances of the limit distributions of Bayesian and maximum likelihood estimators are also provided.