Fitting spatial max-mixture processes with unknown extremal dependence class: an exploratory analysis tool

A flexible model called the max-mixture model has been introduced for modeling situations where the extremal dependence structure type may vary with distance. In this paper, we propose a novel estimation procedure for spatial max-mixture model parameters. Our procedure is based on the madogram, a dependence measure used in geostatistics to describe spatial structures. A nonlinear least squares minimization procedure is applied to obtain the estimators for extremal dependence functions. A simulation study shows that the proposed procedure works well for these models. In an analysis of monthly maxima of daily rainfall data collected over the East of Australia, we implement the proposed estimation procedure for diagnostic and confirmatory purposes.