Home | Career | Grants | Journals | Presentations | Publications | Teaching
|
Statistical Methods for Clusters of Extreme Values
Abstract Extreme values in sequences of independent random variables tend to occur in isolation; for sequences of serially dependent variables, extremes can occur in clusters. Extreme-value theory is well developed for stationary processes and provides mathematical characterisations of the clustering of extremes. Such characterisations are useful models for the extremal behaviour of physical processes: consider storms, floods and droughts for example. Statistical applications harness extreme-value theory to make inferences about the extremes of a process based on a finite sample of data. This thesis addresses several topics in the analysis of clusters of extreme values from both univariate and multivariate processes. Key developments are the following: a theoretically justified scheme for identifying clusters in a sample; estimators for the extremal index that do not require clusters to be identified; a semi-parametric estimator for multivariate extreme-value densities; estimators for cluster summaries that exploit the asymptotic structure of clusters; and a method for modelling clusters in multivariate processes. |
Complete thesis
[pdf]
[ps]
0. Abstract, contents etc. [pdf] [ps] 2. Background Theory & Methods I [pdf] [ps] 3. Background Theory & Methods II [pdf] [ps] 4. Declustering & the Extremal Index [pdf] [ps] 5. Modelling Componentwise Maxima [pdf] [ps] 6. Estimating Cluster Functionals [pdf] [ps] |