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

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Abstract

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.

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Acknowledgements

This work has been supported by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). It was also partly supported by the CERISE LEFE-INSU project. We would like to thank Jean-Noël Bacro, Carlo Gaetan, and Gwladys Toulemonde for providing their C codes which used as a preliminary version for parametric estimation using composite likelihood. We are also very grateful to an editor and to two anonymous reviewers for many helpful comments that have led to considerable improvements in the manuscript.

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  1. Université Claude Bernard Lyon 1, Institute Camille Jordan ICJ UMR 5208 CNRS, Université de Lyon, Lyon, France

    A. Abu-Awwad, V. Maume-Deschamps & P. Ribereau

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  1. A. Abu-Awwad
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  2. V. Maume-Deschamps
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  3. P. Ribereau
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Correspondence to A. Abu-Awwad.

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Abu-Awwad, A., Maume-Deschamps, V. & Ribereau, P. Fitting spatial max-mixture processes with unknown extremal dependence class: an exploratory analysis tool. TEST 29, 479–522 (2020). https://doi.org/10.1007/s11749-019-00663-5

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