Asymptotics for statistical functionals of long-memory sequences

Eric Beutner*, Wei Biao Wu, Henryk Zhle

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

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.

Original languageEnglish
Pages (from-to)910-929
Number of pages20
JournalStochastic Processes and Their Applications
Volume122
Issue number3
DOIs
Publication statusPublished - 1 Mar 2012
Externally publishedYes

Keywords

  • Degenerate V-statistic
  • L-statistic
  • Linear long-memory sequence
  • Modified Functional Delta Method
  • Noncentral limit theorem
  • Quasi-Hadamard differentiability
  • U- and V-statistics
  • Weighted empirical process

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