GRANIČNE RASPODELE PARCIJALNIH MAKSIMUMA RAVNOMERNIH AR (1) PROCESA

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GRANIČNE RASPODELE PARCIJALNIH MAKSIMUMA RAVNOMERNIH AR (1) PROCESA

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dc.contributor.advisor Mladenović, Pavle
dc.contributor.author Glavaš, Lenka
dc.date.accessioned 2017-04-24T14:35:50Z
dc.date.available 2017-04-24T14:35:50Z
dc.date.issued 2015
dc.identifier.uri http://hdl.handle.net/123456789/4454
dc.description.abstract The subject of this doctoral dissertation is related to the problems of extreme values in strictly stationary random sequences. It belongs to the topical area of probability and statistics, broadly applicable to real life situations and in many scienti c elds. It relies on large number of seminal articles and monographs. The main aim of the dissertation is to determine the asymptotic behavior of maxima of some incomplete samples from the rst-order auto-regressive processes with uniform marginal distributions. The dissertation consists of three chapters. New results (the theoretical ones and the results of computer simulations) are presented in the third chapter. Two types of the uniform ARp1q process pXnqnPN are considered: positively correlated and negatively correlated process, with the lag one correlation p1q : CorrpXn 1;Xnq equal to 1 r and 1 r , respectively, where r ¥ 2 is the parameter of the underlying process. Let pcnqnPN be a non-random 0 1 sequence, such that lim nÑ8 1 n n ¸j 1 cj p P r0; 1s. This sequence of degenerate random variables is introduced with the purpose to correspond to the sequence pXnq in the following sense: r.v. Xj is observed if cj 1, otherwise r.v. Xj is not observed (missing observation). Let us use the notation: the r.v. Mn : max 1¤j¤n Xj is maximum of the complete (size n) sample from the random sequence pXnq, and the r.v. Mn is what is called partial maximum, i.e. the maximal element of incomplete sample tXj : cj 1; 1 ¤ j ¤ nu. Based on di erent, speci c deterministic sequences pcnq it is proved that the limiting distribution, as n Ñ 8, of the two-dimensional random vector Mn;Mn , is not uniquely determined by the limit value p. This appears as a consequence of the fact that for the uniform ARp1q process one of the weak dependence conditions does not apply. Namely, the uniform ARp1q process does not satisfy the local condition under which clustering of extremes is restricted. As a consequence of this property, some interesting conclusions about asymptotic joint distributions of random variables Mn and Mn are reached. In the cases when the partial maximum Mn is determined by an arbitrary point process there are presented results obtained by simulations. The rst two chapters are rather informative. Having in mind interest in studying the asymptotic behavior of linearly standardized two-dimensional component-wise maxima the role of the rst chapter is to anticipate the concept of multivariate extreme values. In the second chapter the basic terms in the time series analysis are formulated, with the accent on the linear stationary models, especially on rst-order auto-regressive models. The special attention is dedicated to the uniform ARp1q processes, their properties and existing results concerning their extremal behavior. Still open questions are mentioned in the conclusion, in the very end of the third chapter. en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2017-04-24T14:35:50Z No. of bitstreams: 1 Doktorska_disertacija_Lenka_Glavas.pdf: 1195918 bytes, checksum: f7115e5dd14cfd57b16419c07aa206cf (MD5) en
dc.description.provenance Made available in DSpace on 2017-04-24T14:35:50Z (GMT). No. of bitstreams: 1 Doktorska_disertacija_Lenka_Glavas.pdf: 1195918 bytes, checksum: f7115e5dd14cfd57b16419c07aa206cf (MD5) Previous issue date: 2015 en
dc.language.iso sr en_US
dc.publisher Beograd en_US
dc.title GRANIČNE RASPODELE PARCIJALNIH MAKSIMUMA RAVNOMERNIH AR (1) PROCESA en_US
mf.author.birth-date 1988
mf.author.birth-place Beograd en_US
mf.author.birth-country Srbija en_US
mf.author.residence-state Srbija en_US
mf.author.citizenship Srpsko en_US
mf.author.nationality Srpkinja en_US
mf.subject.area Mathematics en_US
mf.subject.keywords Asymptotic theory; extreme values; missing observations; partial maximum; uniform AR (1) processes en_US
mf.subject.subarea Probability and Statistics en_US
mf.contributor.committee Mladenović, Pavle
mf.contributor.committee Janković, Slobodanka
mf.contributor.committee Petrović, Ljiljana
mf.university.faculty Mathematical Faculty en_US
mf.document.pages 125 en_US
mf.document.location Beograd en_US
mf.document.genealogy-project No en_US
mf.university Belgrade University en_US

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