統計数学セミナー
Seminar on Probability and Statistics |
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Seminar on Probability and Statistics Friday November 27 2009 Tokyo 128 1:40-2:50 pm
非線形時系列モデルのイノベーション密度の推定
加藤 賢悟 / KATO Kengo 広島大学大学院理学研究科数学専攻 / Department of Mathematics, Graduate School of Science, Hiroshima University 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.
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