In this thesis we deal with statistical inference related to extreme value phenomena.
Specifically, if X is a random vector with values in d-dimensional space, our goal is
to estimate moments of ψ(X) for a suitably chosen function ψ when the magnitude
of X is big. We employ the powerful tool of regular variation for random variables,
random vectors and time series to formally define the limiting quantities of interests
and construct the estimators. We focus on three statistical estimation problems: (i)
multivariate tail estimation for regularly varying random vectors, (ii) extremogram
estimation for regularly varying time series, (iii) estimation of the expected shortfall
given an extreme component under a conditional extreme value model. We establish asymptotic normality of estimators for each of the estimation problems. The theoretical findings are supported by simulation studies and the estimation procedures are applied to some financial data.
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/35649 |
| Date | January 2017 |
| Creators | Tong, Zhigang |
| Contributors | Kulik, Rafal |
| Publisher | Université d'Ottawa / University of Ottawa |
| Source Sets | Université d’Ottawa |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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