Statistical analysis of the tail behaviour of dependent sequences

doctoral thesis

• Title (croatian): Statistička analiza repnog ponašanja zavisnih nizova
• Author: Darko Brborović
• Mentor: Bojan Basrak (mentor)
• Committee member: Miljenko Huzak (predsjednik povjerenstva)
• Committee member: Hrvoje Planinić (član povjerenstva)
• Committee member: Azra Tafro (član povjerenstva)
• Committee member: Bojan Basrak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-12-07, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics
• Universal decimal classification (UDC): 51 - Mathematics

Abstract

In this thesis we analyse the tail behaviour of bivariate random sequences, including the stationary \(M\)-dependent sequences, \(M \in \mathbb{N}\). Statistical analysis of the asymptotic tail behaviour of random sequences is often done within the theory of point processes. However, if a larger number of tail events is available it is possible to obtain convergence results towards normal distribution, which we do in this thesis. Motivated by the recent results of DiCiccio and Romano [8] on permutation tests for correlation between random variables, we present and analyse the permutation test of tail dependence for independent and identically distributed bivariate random vectors. Additionally, we present the permutation test of independence for stationary \(M\)-dependent random sequences.

Abstract (croatian)

U ovom radu predstavljamo analizu repnog ponašanja slučajnih nizova dvodimenzionalnih vektora, što uključuje i slučaj stacionarnih \(M\)-zavisnih nizova, \(M \in \mathbb{N}\). Često se asimptotska analiza repnog ponašanja slučajnih nizova obavlja u okviru teorije točkovnih procesa. Ipak, ukoliko je dostupan veći broj repnih događaja moguće je postići konvergenciju prema normalnoj distribuciji, kao što je to slučaj u ovom radu. Motivirani relativno novim rezultatima o permutacijskim testovima za korelaciju između dvije slučajne varijable, objavljenima u DiCiccio and Romano [8], u ovom radu predstavljamo i analiziramo test repne zavisnosti za nezavisne i jednako distribuirane dvodimenzionalne slučajne vektore. Dodatno, predstavljamo i permutacijski test nezavisnosti za stacionarne \(M\)-zavisne slučajne nizove.

• Keywords: tail behavior of bivariate random sequences; statistical analysis
• Keywords (croatian): repno ponašanje slučajnih nizova; dvodimenzionalni vektori; statistička analiza
• Language: english
• URN:NBN: urn:nbn:hr:217:640209
• Study programme: Title: Mathematics; Study programme type: university; Study level: postgraduate; Academic / professional title: doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika (doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika)
• Type of resource: Text
• Extent: v, 110 str.
• File origin: Born digital
• Access conditions: Open access
• Created on: 2023-03-01 12:09:47