On the limiting behavior of the Pickands estimator for bivariate extreme-value distributions

Estimating the tail-dependence coefficient: Properties and pitfalls

“…See, for instance, Tiago de Oliveira (1984), Tawn (1988), Smith et al (1990), Hutchinson and Lai (1990) or Coles and Tawn (1991) for fitting parametric (structural) models to A. By contrast, Pickands (1981), Deheuvels (1991), Joe et al (1992), Abdous et al (1998), or Falk and Reiss (2003) consider nonparametric estimation procedures.…”

Non-Parametric Inference for Bivariate Extreme-Value Copulas

“…This observation was confirmed for a wide range of models and parameter values through extensive numerical studies. It was also seen to hold for the endpoint-corrected estimators A P n,c and A CFG n,c originally proposed by Deheuvels (1991) and by Capéraà et al (1997), respectively. It may be conjectured, therefore, that P-c * → CFG-c and P-opt * → CFG-opt.…”

“…Before proceeding, however, endpoint corrections will be discussed briefly. In order to overcome this defect, Deheuvels (1991) introduced the estimator…”

“…. , (X n , Y n ) from H has been considered successively by Pickands (1981), Deheuvels (1991), Capéraà et al (1997), Jiménez et al (2001), Hall and Tajvidi (2000), and Segers (2007). In these papers, the margins F and G are assumed to be known, so that in effect, a random sample (F (X 1 ), G(Y 1 )), .…”

A Karhunen–Loeve decomposition of a Gaussian process generated by independent pairs of exponential random variables

“…We note that, when combined with the SLLN for X n and Y n , the results of [17] imply readily that, for an arbitrary dependence function A fulfill-…”