Information theoretic approach to statistics of extremes with applications in risk analysis, insurance and environment

Extreme Value Theory is a special field of statistics which is often used in modelingand analyzing behavior of extreme and rare events. This theory has well-establishedtheoretical foundations, and it finds fruitful applications in various fields of science. Thesefields include, but are not limited to, finance and insurance, information technology andtelecommunications, environmental science, wind engineering and aerodynamics, foodscience, biomedical and clinical data processing, DNA analysis, and management.Despite the well-established theoretical foundations, researchers still tend to encountera number of issues when trying to solve practical problems using the ExtremeValue Theory. These problems are often associated with limitations of common estimators.For instance, the maximum likelihood method fails to meet the regularity conditionsfor a range of values of underlying parameters of Extreme Value Models. Method of Momentsand its variations are often advocated as `viable' alternatives to the maximumlikelihood method, but, in some cases, they tend to yield nonsensical parameter estimateswhich tend contradict the data used in estimations. In addition, the common estimationmethods suffer from other serious shortcomings as well: including sensitivity of parameterestimates, convergence problems, tendency to misspecify submodels of Extreme ValueDistributions, and complexity caused by strict functional and distributional assumptions.This dissertation uses info-metrics framework to develop new estimation methodsfor Extreme Value Models. Main motivations are as follows: (a) the info-metrics frameworkrelaxes rigid assumptions inherent in the common estimation methods, e.g. the rigidassumption of strict fulfillment of zero-moment conditions; (b) the info-metrics frameworkprovides convenient tools to deal with the under-determined problems; (c) the frameworkalso allows researchers to address the fundamental uncertainty related to model discrimination;(d) the framework can be beneficial in cases where the data is noisy; (e) theinfo-metrics framework also allows to incorporate covariates and regressors into ExtremeValue Models without adding complexity.Simulation results and empirical examples of this dissertation demonstrate thatthe flexibility of the info-metrics framework can address several shortcomings of commonestimators of Extreme Value Models: (a) reduces sensitivity of parameter estimates; (b)mitigates the problem of misspecication of submodels of Extreme Value Distributions; (c)demonstrates superior performance compared to common estimations methods, especiallyin cases where the sample size is small, and the data is noisy; (d) in many cases, the info-metricsframework is able to achieve the desired finite-sample properties and empiricalconclusions without making strict assumption regarding the data-generating process.