An M‐estimator of spatial tail dependence

By John H. J. Einmahl, Anna Kiriliouk, A. Krajina, Johan Segers. 2014

54 citations recorded by the source corpus.

Tail dependence models for distributions attracted to a max‐stable law are fitted by using observations above a high threshold. To cope with spatial, high dimensional data, a rank‐based M‐estimator is proposed relying on bivariate margins only. A data‐driven weight matrix is used to minimize the asymptotic variance. Empirical process arguments show that the estimator is consistent and asymptotically normal. Its finite sample performance is assessed in simulation experiments involving popular max‐stable processes perturbed with additive noise. An analysis of wind speed data from the Netherlands illustrates the method.

Subfields: Economics and Econometrics, Finance, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/9f0f296e327bf3ea8c0c8d7b41eef82c2ad1d5da

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

1. A. C. Davison
2. Raphaël Huser
3. Thomas Opitz
4. Emeric Thibaud
5. Raphaël de Fondeville
6. Sebastian Engelke
7. Johan Segers
8. Adrien Hitz

In Finance

1. Raphaël Huser
2. Thomas Opitz
3. A. C. Davison
4. Emeric Thibaud
5. Sebastian Engelke
6. Raphaël de Fondeville
7. Johan Segers
8. Adrien Hitz

In Global and Planetary Change

1. Raphaël Huser
2. Thomas Opitz
3. A. C. Davison
4. Sebastian Engelke
5. Emeric Thibaud
6. Adrien Hitz
7. Raphaël de Fondeville
8. Johan Segers

Citations in the corpus

• Extremes on river networks (2015, methodology): “As also noted by Engelke et al. (2015) and Einmahl et al. (2015), the estimates of λEuc have larger variation than the others.”
• A continuous updating weighted least squares estimator of tail dependence in high dimensions (2016, methodology): “Figure 1 shows the RMSE of three estimators based on the empirical tail dependence function: the two extremal coefficients estimators mentioned above and the pairwise M-estimator of Einmahl et al. (2016) as implemented in the R package tailDepFun (Kiriliouk 2016).”
• Functional peaks‐over‐threshold analysis (2020, methodology): “Alternatives involve censoring of low components (e.g., Wadsworth & Tawn, 2014), composite likelihoods (Castruccio et al., 2016; Huser & Davison, 2013; Padoan et al., 2010) or M-estimation using pairwise tail indexes (Einmahl et al., 2016a,b).”
• Graphical models for extremes (2018, methodology): “Alternative methods use M-estimators (Einmahl et al., 2012, 2016) or proper scoring rules (de Fondeville and Davison, 2018).”
• Multivariate peaks over thresholds models (2016, unknown): “A companion paper (Kiriliouk et al. 2016) addresses practical modelling aspects.”
• Modeling asymptotically independent spatial extremes based on Laplace random fields (2015, unknown): “Recent studies on similar data (Engelke et al., 2015; Einmahl et al., 2015; Oesting et al., 2015) are based on max-stable models without challenging the assumption of asymptotic dependence.”
• Bridging asymptotic independence and dependence in spatial extremes using Gaussian scale mixtures (2016, methodology): “ll uncensored density when the observation vector is a partial exceedance of the multivariate threshold or by using robust M-estimators based on ranks and bivariate tail characteristics as proposed inEinmahl et al. (2016) for max-stable models to avoid costly high-dimensional numerical integration. ”