Asymptotics for statistical functionals of long-memory sequences

Eric Beutner, Wei Biao Wu and Henryk Zähle

Stochastic Processes and their Applications, 2012, vol. 122, issue 3, 910-929

Abstract: We present two general results that can be used to obtain asymptotic properties for statistical functionals based on linear long-memory sequences. As examples for the first one we consider L- and V-statistics, in particular tail-dependent L-statistics as well as V-statistics with unbounded kernels. As an example for the second result we consider degenerate V-statistics. To prove these results we also establish a weak convergence result for empirical processes of linear long-memory sequences, which improves earlier ones.

Keywords: Noncentral limit theorem; Linear long-memory sequence; Quasi-Hadamard differentiability; Modified Functional Delta Method; Weighted empirical process; L-statistic; U- and V-statistics; Degenerate V-statistic (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:122:y:2012:i:3:p:910-929

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DOI: 10.1016/j.spa.2011.10.006

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