Ocenjivanje indeksa repa raspodele korišćenjem nekompletnih uzoraka
On tail index estimation using samples with missing observations
Author
Ilić, Ivana
Mentor
Mladenović, PavleCommittee members
Janković, SlobodankaPetrović, Ljiljana
Metadata
Show full item recordAbstract
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...