Title: A framework for spatio-temporal regression analysis of extremes in a presence of missing covariates
Authors: Olga Kaiser - Universita della Svizzera italiana (Switzerland) [presenting]
Illia Horenko - Universita della Svizzera italiana (Germany)
Abstract: Statistical regression analysis of extreme events aims to describe their behavior as a relationship between some covariates and the observed extremes. Often the complete set of all the significant covariates can not be provided. In such a case nonstationary and nonparametric approaches are required to obtain unbiased results. Based on the Generalized Extreme Value distribution (GEV) and the nonparametric Finite Element time-series analysis Methodology (FEM) with Bounded Variation on the model parameters (BV) we build a semiparametric, nonstationary, and non-homogenous computational framework for regression analysis of spatio-temporal extremes. The FEM-BV-GEV framework addresses the issue of nonstationarity with describing the underlying dynamics by $K\geq 1$ local stationary models and a nonstationary, nonparametric and nonhomogenous switching process. The switching process can provide insights into the pattern of the systematically missing covariates. We show cases when the analysis of the switching process reveals explicitly the missing covariate. Further, the framework provides a spatio-temporal clustering of extreme events and so a pragmatic, nonparametric and nonstationary description of the underlying spatial dependence structure. The performance of the framework is demonstrated on monthly maximum temperature data over Europe.