Tail estimation based on numbers of near m-extremes

Samuel Müller*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Let {Xn,n⩾1} be a sequence of independent random variables with common continuous distribution function F having finite upper endpoint. A new tail index estimator γ^ n is defined based on only two numbers of near m-extremes
Kn(ai,m)=\# {j:X(n−m+:1)−ai<Xj⩽X(n−m+1:n)},m⩾1

where X (i:n) denotes the -th order statistic and a 2 > a 1 > 0. The weak and almost sure convergence of γ^ n to the tail index γ, as well as the asymptotic distribution is given. Moreover, the asymptotic distribution of K n (a n , m) for a n → 0 is derived.
Original languageEnglish
Pages (from-to)197-210
Number of pages14
JournalMethodology and Computing in Applied Probability
Issue number2
Publication statusPublished - Jun 2003
Externally publishedYes


  • extreme value theory
  • near extremes
  • tail index estimation


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