A Model-Free Selection Criterion For The Mixing Coefficient Of Spatial Max-Mixture Models

TL;DR

This paper introduces a nonparametric, model-free method for selecting the mixing coefficient in spatial max-mixture models, improving the modeling of extremal dependence in geostatistics.

Contribution

It proposes a novel selection criterion based on madograms, derived from a nonlinear least squares approach, for better estimation of extremal dependence structures.

Findings

Effective in simulation studies

Successfully applied to Australian precipitation data

Enhances flexibility in modeling spatial extremes

Abstract

One of the main concerns in extreme value theory is to quantify the dependence between joint tails. Using stochastic processes that lack flexibility in the joint tail may lead to severe under-or over-estimation of probabilities associated to simultaneous extreme events. Following recent advances in the literature, a flexible model called max-mixture model has been introduced for modeling situations where the extremal dependence structure may vary with the distance. In this paper we propose a nonparametric model-free selection criterion for the mixing coefficient Our criterion is derived from a madogram, a notion classically used in geostatistics to capture spatial structures. The procedure is based on a nonlinear least squares between the theoretical madogram and the empirical one. We perform a simulation study and apply our criterion to daily precipitation over the East of Australia.