Abstract
The tail correlation function (TCF) is a popular bivariate extremal dependence measure to summarize data in the domain of attraction of a max-stable process. For the class of TCFs, being largely unexplored so far, several aspects are contributed: (i) generalization of some mixing max-stable processes (ii) transfer of two geostatistical construction principles to max-stable processes, including the turning bands operator (iii) identification of subclasses of TCFs, including M3 processes based on radial monotone shapes (iv) recovery of subclasses of max-stable processes from TCFs (v) parametric classes (iv) diversity of max-stable processes sharing an identical TCF. We conclude that caution should be exercised when using TCFs for statistical inference.
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Strokorb, K., Ballani, F. & Schlather, M. Tail correlation functions of max-stable processes. Extremes 18, 241–271 (2015). https://doi.org/10.1007/s10687-014-0212-y
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DOI: https://doi.org/10.1007/s10687-014-0212-y
Keywords
- Brown-Resnick
- Extremal coefficient
- Mixed moving maxima
- Poisson storm
- Stationary truncation
- Tail dependence
- Turning bands