Seminar on Probability and Statistics

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

2009/11/27

13:40-14:50   Room #128 (Graduate School of Math. Sci. Bldg.)
加藤 賢悟 (広島大学大学院理学研究科数学専攻)
非線形時系列モデルのイノベーション密度の推定
[ Abstract ]
In this talk, we consider the problem of estimating the innovation density in nonlinear autoregressive models. Specifically, we establish the convergence rate of the supremum distance between the residual-based kernel density estimator and the kernel density estimator using the unobservable actual innovation variables. The proof of the main theorem relies on empirical process theory instead of the conventional Taylor expansion approach. As applications, we obtain the exact rate of weak uniform consistency on the whole line, pointwise asymptotic normality of the residual-based kernel density estimator and the asymptotic distribution of a Bickel-Rosenblatt type global measure statistic related to it. We also examine the conditions of the main theorem for some specic time series model.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/09.html