Journal of Theoretical Probability

, Volume 31, Issue 2, pp 853–866 | Cite as

On the Asymptotic Locations of the Largest and Smallest Extremes of a Stationary Sequence

  • Luísa Pereira


This paper deals with the asymptotic independence of the normalized kth upper- and rth lower-order statistics and their locations, defined on some strictly stationary sequences \(\left\{ X_n\right\} _{n\ge 1}\) admitting clusters of both high and low values. The main result is the asymptotic independence of the joint locations of the k-largest extremes and the joint locations of the r-smallest extremes of \(\left\{ X_{n}\right\} _{n\ge 1}\), which allows us to censor a sample, by ensuring that the set of observations that we selected contains the k-largest and r-smallest order statistics of the stationary sequence \(\left\{ X_{n}\right\} _{n\ge 1}\) with a predetermined probability.


Exceedances Locations of extremes Dependence conditions Point processes 

Mathematics Subject Classification (2010)

60G70 60G55 



The author would like to thank the referees for several corrections and important suggestions which significantly improved this paper. This work was partially supported by National Foundation of Science and Technology through UID/MAT/00212/2013.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Centro de Matemática e Aplicações (CMA-UBI)Universidade da Beira InteriorCovilhãPortugal

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