Maxima and minima of complete and incomplete stationary sequences

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Serval ID
serval:BIB_6EDF16449105
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Maxima and minima of complete and incomplete stationary sequences
Journal
Stochastics An International Journal of Probability and Stochastic Processes
Author(s)
Hashorva E., Weng Z.
ISSN
1744-2508 (Print)
1744-2516 (Electronic)
Publication state
Published
Issued date
2014
Peer-reviewed
Oui
Volume
86
Number
5
Pages
707-720
Language
english
Abstract
In the seminal contribution [R. A. Davis, Maxima and minima of stationary sequences, Ann. Probab. 7(3) (1979), pp. 453-460.] the joint weak convergence of maxima and minima of weakly dependent stationary sequences is derived under some mild asymptotic conditions. In this paper we address additionally the case of incomplete samples assuming that the average proportion of incompleteness converges in probability to some random variable P. We show the joint weak convergence of the maxima and the minima of both complete and incomplete samples. It turns out that the maxima and the minima are asymptotically independent when P is a deterministic constant.
Keywords
Maxima, Minima, Incomplete sample, Joint limit distribution, Stationary sequences, Berman condition, Gaussian ARMA processes
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Create date
14/12/2013 15:39
Last modification date
20/08/2019 14:28
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