The difference of symmetric quantiles under long range dependence

G. Tarr*, N. C. Weber, S. Müller

*Corresponding author for this work

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

This paper investigates two robust estimators of the scale parameter given data from a stationary, long range dependent Gaussian process. In particular the limiting distributions of the interquartile range and related τ-quantile range statistics are established. In contrast to single quantiles, the limiting distribution of the difference of two symmetric quantiles is determined by the level of dependence in the underlying process. It is shown that there is no loss of asymptotic efficiency for the τ-quantile range relative to the standard deviation under extreme long range dependence which is consistent with results found previously for other estimators of scale.

Original languageEnglish
Pages (from-to)144-150
Number of pages7
JournalStatistics and Probability Letters
Volume98
DOIs
Publication statusPublished - Mar 2015
Externally publishedYes

Keywords

  • Interquartile range
  • Long range dependence
  • Pairwise means
  • U-statistics

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