Statistical analysis of extreme values in spatio-temporal processes= Análisis estadístico de valores extremos en procesos espacio-temporales.

Abstract

This thesis work has been developed in the framework of granted projects P05-FQM-09900 and P08-FQM-03834 of Consejería de Innovación, Ciencia y Empresa, Junta de Andalucía, and MTM2009-13250 of Ministerio de Ciencia e Innovación, Spain. The title of the thesis, "Statistical Analysis of Extreme Values in Spatio-Temporal Processes", makes reference to a broad context, of increasing relevance in current statistical and modeling research, in which various aspects of interest have been investigated. Specifically, the following topics are the main object of this research: - Analysis of geometrical characteristics of spatial threshold exceedance sets. Effect of deformation and blurring transformations. - Application of (marked) point process techniques to the analysis of distribution patterns in spatial threshold exceedance sets. - Wavelet analysis of temporal intermittency and the effect of time deformation. - Block thresholding techniques based on entropy criteria for spatial correlated shrinkage. - Extended formulation of blur-generated space-time models involving dynamical deformation. In particular, differential aspects in relation to underlying model properties such as local variability and dependence ranges, as well as to threshold specifications, are explored.