Electronic Journal of Statistics

The spectrogram: A threshold-based inferential tool for extremes of stochastic processes

Thomas Opitz, Jean-Noël Bacro, and Pierre Ribereau

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We extend the statistical toolbox for inferring the extreme value behavior of stochastic processes by defining the spectrogram. It is based on a pseudo-polar representation of bivariate data and represents a collection of spectral measures that characterize the bivariate extremal dependence structure in terms of a univariate distribution. Based on threshold exceedances in the original event data, estimation of the spectrogram is flexible and efficient. The virtues of the spectrogram for exploratory studies and for parametric inference are highlighted. We propose a variance reduction technique that can be applied to the estimation of summary statistics like the extremogram. Parametric inference based on distance measures between the empirical and the model spectrogram, as for instance pairwise likelihoods or least squares distances, is developed. Simulated data illustrate gains in parametric estimation efficiency compared to a standard estimation approach. An application to precipitation data collected in the Cévennes region in France shows the practical utility of the introduced notions.

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Electron. J. Statist., Volume 9, Number 1 (2015), 842-868.

First available in Project Euclid: 20 April 2015

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Max-stable processes pairwise inference spatial extremes spectral measure variance reduction


Opitz, Thomas; Bacro, Jean-Noël; Ribereau, Pierre. The spectrogram: A threshold-based inferential tool for extremes of stochastic processes. Electron. J. Statist. 9 (2015), no. 1, 842--868. doi:10.1214/15-EJS1021. https://projecteuclid.org/euclid.ejs/1429536044

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