TY - JOUR

T1 - Extremes of order statistics of stationary processes

AU - Dȩbicki, Krzysztof

AU - Hashorva, Enkelejd

AU - Ji, Lanpeng

AU - Ling, Chengxiu

N1 - Publisher Copyright:
© 2014, Sociedad de Estadística e Investigación Operativa.

PY - 2015/6/26

Y1 - 2015/6/26

N2 - Let (Formula presented.) be independent copies of a stationary process (Formula presented.). For given positive constants u,T, define the set of rth conjunctions (Formula presented.) with (Formula presented.) the rth largest order statistics of (Formula presented.). In numerous applications such as brain mapping and digital communication systems, of interest is the approximation of the probability that the set of conjunctions (Formula presented.) is not empty. Imposing the Albin’s conditions on X, in this paper we obtain an exact asymptotic expansion of this probability as u tends to infinity. Furthermore, we establish the tail asymptotics of the supremum of the order statistics processes of skew-Gaussian processes and a Gumbel limit theorem for the minimum order statistics of stationary Gaussian processes.

AB - Let (Formula presented.) be independent copies of a stationary process (Formula presented.). For given positive constants u,T, define the set of rth conjunctions (Formula presented.) with (Formula presented.) the rth largest order statistics of (Formula presented.). In numerous applications such as brain mapping and digital communication systems, of interest is the approximation of the probability that the set of conjunctions (Formula presented.) is not empty. Imposing the Albin’s conditions on X, in this paper we obtain an exact asymptotic expansion of this probability as u tends to infinity. Furthermore, we establish the tail asymptotics of the supremum of the order statistics processes of skew-Gaussian processes and a Gumbel limit theorem for the minimum order statistics of stationary Gaussian processes.

KW - Albin’s conditions

KW - Conjunction

KW - Generalized Albin constant

KW - Gumbel limit theorem

KW - Order statistics process

KW - Skew-Gaussian process

UR - http://www.scopus.com/inward/record.url?scp=84929841954&partnerID=8YFLogxK

U2 - 10.1007/s11749-014-0404-4

DO - 10.1007/s11749-014-0404-4

M3 - Article

AN - SCOPUS:84929841954

SN - 1133-0686

VL - 24

SP - 229

EP - 248

JO - Test

JF - Test

IS - 2

ER -