Title: Asymptotic error bound approximation of threshold exceedance probabilities for non-stationary random fields
Authors: Jose Luis Romero - University of Granada (Spain) [presenting]
Jose Miguel Angulo - University of Granada (Spain)
Abstract: Evaluation of different forms of threshold exceedance probabilities, for large thresholds in general scenarios, is one of the most relevant problems arising in the assessment of extremal behaviour in real phenomena. Euler-Poincare characteristic (EPC) is a structural property of excursion sets, intrinsically related to these probabilities. There is a vast literature related to providing error bound approximations between excursion probabilities and EPC under Gaussian and/or stationary assumptions for the underlying random field model, with increasing interest in more general scenarios. Spatial deformation is used in fields such as image analysis, environmental studies, etc. as an approach to represent heterogeneities of a reference stationary random field. Local smoothing by means of a kernel-based blurring transformation in terms of a convolution operator is also used in real applications. From both transformations, significant classes of non-stationary random fields arise. There exist kernel-based regularizing sequences providing different forms of convergence to the random field reference model, by means of the derived blurred sequence. Asymptotic error bound approximations for non-regular random fields obtained under spatial deformation and blurring transformations of the reference model are extended. Effects of regularizing sequences such as, the so-called, Mollifiers and Gaussian kernels, is analyzed and illustrated by simulation for different scenarios.