An M-Estimator for Tail Dependence in Arbitrary Dimensions
By John H. J. Einmahl, A. Krajina, Johan Segers. 2011
115 citations recorded by the source corpus.
Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as the value that minimizes the distance between a vector of weighted integrals of the tail dependence function and their empirical counterparts. The minimization problem has, with probability tending to one, a unique, global solution. The estimator is consistent and asymptotically normal. The spectral measures of the tail dependence models to which the method applies can be discrete or continuous. Examples demonstrate the applicability and the performance of the method.
Subfields: Finance, Statistics and Probability, Signal Processing
View Paper: https://www.semanticscholar.org/paper/0444d8317a1fdc7f77bf89c26455e374f64414be
Citations in the corpus
- MAX-STABLE MODELS FOR MULTIVARIATE EXTREMES (2012, unknown): “Max-stable models with discrete spectral measures are called extreme-value factor models in Einmahl et al. (2011). Each of the m possible outcomes ak results”
- Multivariate peaks over thresholds models (2016, unknown): “Other papers consider nonparametric or semiparametric rank-based PoT methods focusing on the dependence structure but largely ignoring modelling the margins (de Haan et al. 2008; Einmahl et al. 2012; Einmahl et al. 2016).”
- An M‐estimator of spatial tail dependence (2014, unknown): “5,2} and (a) d D 4 and (b) d D 6 for the d-dimensional Smith model on the line ( , pairwise estimator with identity weight matrix; , pairwise estimator with optimal weight matrix; , d-dimensional M -estimator from Einmahl et al. (2012)), and (c) asymptotic variance M.”
- A continuous updating weighted least squares estimator of tail dependence in high dimensions (2016, unknown): “Such functions arise in max-linear models (Wang and Stoev, 2011), in particular factor models (Einmahl et al., 2012) or structural equation models based on directed acyclic graphs (Gissibl and Klüppelberg, 2015).”