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

Jannis Buchsteiner

Statistics & Probability Letters, 2015, vol. 96, issue C, 170-179

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.

Keywords: Sequential empirical process; Long-range dependence; Weighted norm; Modified functional delta method (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spl.2014.09.022

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