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Ocenjivanje indeksa repa raspodele korišćenjem nekompletnih uzoraka

On tail index estimation using samples with missing observations

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2013
Disertacija.pdf (3.099Mb)
Author
Ilić, Ivana
Mentor
Mladenović, Pavle
Committee members
Janković, Slobodanka
Petrović, Ljiljana
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Abstract
Teza obrađuje ocenjivanje indeksa pravilne promenljivosti na nekompletnom uzorku zavisnih slučajnih veličina sa raspodelom teškog repa. Pod pretpostavkom ekstremalne zavisnosti dokazuje se konzistentnost ocene geometrijskog tipa, kao i konzistentnost i asimptotska normalnost Hilove ocene. Navode se primeri procesa koji zadovoljavaju zahteve dokazanih teorema i na kojima se mogu primeniti dobijeni rezultati...
For the sequence of heavy-tailed and possibly dependent random variables with the missing observations the estimation of the tail-index is considered. Under minimal but verifiable assumption of ''extremal dependence'' we proved the consistency of geometric-type estimator (Brito and Freitas, 2003). We extended results from Mladenovic and Piterbarg (2008) and proved the consistency and the asymptotic normality of the Hill estimator. Illustrative examples are provided...
Faculty:
University of Belgrade, Faculty of Mathematics
Date:
04-03-2013
Keywords:
Hilova ocena / Hill estimator / nekompletni uzorci / indeks repa raspodele / ocena geometrijskog tipa / ekstremalna zavisnost / incomplete samples / tail index / geometric-type estimator / extremal dependence
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URI
http://nardus.mpn.gov.rs/handle/123456789/2849
http://eteze.bg.ac.rs/application/showtheses?thesesId=1714
https://fedorabg.bg.ac.rs/fedora/get/o:9292/bdef:Content/download
http://vbs.rs/scripts/cobiss?command=DISPLAY&base=70036&RID=45439503

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