統計数学セミナー

過去の記録 ~04/21次回の予定今後の予定 04/22~

担当者 吉田朋広、荻原哲平、小池祐太
セミナーURL http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/
目的 確率統計学およびその関連領域に関する研究発表, 研究紹介を行う.

2009年11月27日(金)

13:40-14:50   数理科学研究科棟(駒場) 128号室
加藤 賢悟 氏 (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
[ 講演概要 ]
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.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/09.html