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

Luísa Pereira ()
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Luísa Pereira: Universidade da Beira Interior

Journal of Theoretical Probability, 2018, vol. 31, issue 2, 853-866

Abstract: Abstract 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 $$\left\{ X_n\right\} _{n\ge 1}$$ X n n ≥ 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 $$\left\{ X_{n}\right\} _{n\ge 1}$$ X n n ≥ 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 $$\left\{ X_{n}\right\} _{n\ge 1}$$ X n n ≥ 1 with a predetermined probability.

Keywords: Exceedances; Locations of extremes; Dependence conditions; Point processes; 60G70; 60G55 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10959-017-0742-8

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