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Weak convergence of the weighted sequential empirical process of some long-range dependent data

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  • Buchsteiner, Jannis

Abstract

Let (Xk)k≥1 be a Gaussian long-range dependent process with EX1=0, EX12=1 and covariance function r(k)=k−DL(k). For any measurable function G let (Yk)k≥1=(G(Xk))k≥1. We study the asymptotic behaviour of the associated sequential empirical process (RN(x,t)) with respect to a weighted sup-norm ‖⋅‖w. We show that, after an appropriate normalization, (RN(x,t)) converges weakly in the space of cádlág functions with finite weighted norm to a Hermite process.

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  • Buchsteiner, Jannis, 2015. "Weak convergence of the weighted sequential empirical process of some long-range dependent data," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 170-179.
    • Handle: RePEc:eee:stapro:v:96:y:2015:i:c:p:170-179
    DOI: 10.1016/j.spl.2014.09.022
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    References listed on IDEAS

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    1. Beutner, Eric & Wu, Wei Biao & Zähle, Henryk, 2012. "Asymptotics for statistical functionals of long-memory sequences," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 910-929.
    2. Beutner, Eric & Zähle, Henryk, 2010. "A modified functional delta method and its application to the estimation of risk functionals," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2452-2463, November.
    3. Berkes, István & Hörmann, Siegfried & Schauer, Johannes, 2009. "Asymptotic results for the empirical process of stationary sequences," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1298-1324, April.
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